General references
Dense QCD reviews
Collaboration papers
Conference papers
Papers
Other papers
LOFF papers
Astrophysical applications
 
 

• J. Polchinski, hep-th/9210046.Effective field theory and the Fermi surface, The method of effective field theory applied to superconductivity. (Lectures presented at TASI 1992)
• R. Shankar. A review of interacting fermions  (Rev. Mod. Phys. 66, 129 (1993))
• V.B. Eltsov, M. Krusius, G.E. Volovik, cond-mat/9809125. Superfluid 3He: a Laboratory Model System of Quantum Field Theory. Recently a new phenomenon was discovered in rotating superfluid 3He-B: the formation of quantized vortices within bulk superflow in the presence of ionizing radiation. This ``mini bang'' allows one to explore the superfluid transition within the clean bulk medium on the microsecond time scale. The experiment appears to provide the first quantitative test of the theories on defect formation in a time-dependent second order phase transition.
• F. Wilczek, hep-ph/9907340. What QCD Tells Us About Nature -- and Why We Should Listen. I discuss why QCD is our most perfect physical theory. Then I visit a few of its current frontiers. Finally I draw some appropriate conclusions. (Nucl. Phys. A663 (2000) 3-20)
• J. Zinn-Justin, hep-ph/0005272. Quantum field theory at finite temperature: an introduction. Review of statistical quantum field theory at equilibrium
• M.-P. Lombardo, hep-ph/0103141. Finite temperature field theory. These lectures review phases and phase transitions of the Standard Model, with emphasis on those aspects which are amenable to a first principle study. Model calculations and theoretical ideas of practical applicability are discussed as well. (lectures given at the Summer School on Astroparticle Physics and Cosmology, ICTP, Trieste, 12-30 June 2000)
• K. Rajagopal and F. Wilczek, hep-ph/0011333.The condensed matter physics of QCD. A complete review of high-density QCD, including CFL, 2SC, LOFF and applications. ('At the Frontier of Particle Physics / Handbook of QCD', M. Shifman, ed., (World Scientific).

In *Shifman, M. (ed.))
• S.H.D. Hsu, hep-ph/0003140.Color superconductivity in high density quark matter. A review of color superconductivity from the point of view of the R-Group. (TMU-Yale Symposium on Dynamics of Gauge Fields)
• H. Satz, hep-ph/0009099. The Search for the QGP: A Critical Appraisal. The start of RHIC this year will increase the highest available collision energy by a factor 10. This seems a good time for a critical assessment: what have we learned so far and what can we hope to learn in the coming years? (Nucl.Phys.Proc.Suppl. 94 (2001) 204-218)
• D.K. Hong, hep-ph/0101025.Aspects of color superconductivity. A review about the evaluation of the gap and of the NG boson masses. (Acta Phys.Polon. B32 (2001) 1253-1276)
• M. Alford, hep-ph/0102047.Color superconducting quark matter. A review of color superconducting phases and applications to compact stars. (Ann.Rev.Nucl.Part.Sci. 51 (2001) 131-160)
• G.E. Brown, Mannque Rho, hep-ph/0103102. On the Manifestation of Chiral Symmetry in Nuclei and Dense Nuclear Matter. his article reviews our view on how chiral symmetry, its pattern of breaking and restoration under extreme conditions manifest themselves in the nucleon, nuclei, nuclear matter and dense hadronic matter. (Physics Reports 363 (2002) 85)
• S. Hands, physics/0105022. The Phase Diagram of QCD. I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma of more elementary constituents called quarks and gluons. (Popular lecture). (Contemporary Physics 42 (2001) 209-225)
• D. F. Litim, C. Manuel, hep-ph/0110104. Semi-classical transport theory for non-Abelian plasmas. We review a semi-classical transport theory for non-Abelian plasmas based on a classical picture of coloured point particles. Within this formalism, kinetic equations for the mean particle distribution, the mean fields and their fluctuations are obtained using an ensemble-average in phase space. The framework permits     the integrating-out of fluctuations in a systematic manner. This leads to the derivation of collision integrals, noise sources and fluctuation-induced currents for the effective transport equations of QCD. (Phys. Rept. 364 (2002) 451-539)
• H. Satz, hep-ph/0201051. States of Strongly Interacting Matter. I discuss the phase structure of strongly interacting matter at high temperatures and densities, as predicted by statistical QCD, and consider in particular the nature of the transition of hot hadronic matter to a plasma of deconfined quarks and gluons. (Fortsch.Phys. 50 (2002) 541-551)
• G. Nardulli, hep-ph/0202037.Effective description of QCD at very high densities. A review of effective field theory applied to color superconductivity. Evaluation of the parameters appearing in the effective lagrangians for the CFL, 2SC and LOFF phases. (Rivitsta del Nuovo Cimento)
• Mannque Rho, nucl-th/0202078.Lectures on effective field theories for nuclei, nuclear matter and dense matter. A review of effective field theory in various domains including high-density QCD.
• Mannque Rho, hep-ph/0206003. The Cheshire Cat Hadrons Revisited. The notion of Cheshire Cat Principle in hadron structure developed in a 1993 lecture note is revisited by correcting nontrivial errors committed in the lecture and bringing up to date with the recent developments on the "vector manifestation" of chiral symmetry a la Harada-Yamawaki. (Corrected and updated version of Phys. Rep. 240 (1994) 1)
• T. Schafer, nucl-th/0208070. EFFECTIVE THEORY OF THE COLOR FLAVOR LOCKED PHASE. 16th International Conference on Ultrarelativistic Nucleus-Nucelus Collisions, Quark Matter 2002 (QM 2002), Nantes, France, 18-24 Jul 2002
  
• K. Rajagopal, SLAC Beam Line 31N2:9-15,2001. Free the quarks. Popular lecture.
• T. Schafer, Nucl.Phys.A702:167-176,2002. THE GROUND STATE OF STRANGE QUARK MATTER. International Symposium On Statistical QCD, 26-30 Aug 2001, Bielefeld, Germany
• S. Reddy, nucl-th/0211045. NOVEL PHASES AT HIGH DENSITY AND THEIR ROLES IN THE STRUCTURE AND EVOLUTION OF NEUTRON STARS. We present a pedagogic discussion on the role of novel phases of dense baryonic matter in ``neutron'' stars. Qualitative aspects of the physics that drives phase transitions and some of its astrophysical consequences are discussed. Observable aspects of neutron star structure and early evolution of the newly born neutron star are discussed in some detail. (lectures presented at the Zakopane Summer School on Flavor Dynamics, 2002)
• D. K. Hong, hep-ph/0301125. Positivity of QCD at asymptotic density. In this talk, I try to show that the sign problem of dense QCD is due to modes whose frequency is higher than the chemical potential. An effective theory of quasi-quarks near the Fermi surface has a positive measure in the leading order. The higher-order corrections make the measure complex, but they are suppressed as long as the chemical potential is sufficiently larger than $\Lambda_{\rm QCD}$. As a consequence of the positivity of the effective theory, we can show that the global vector symmetries except the U(1) baryon number are unbroken at asymptotic density (contribution to Strong and Electroweak Matter '02 (Heidelberg))
• R. Casalbuoni, hep-ph/0301162. Anisotropic Color Superconductivity. We discuss the possibility that in finite density QCD an anisotropic phase is realized. This case might arise for quarks with different chemical potential and/or different masses. In this phase crystalline structures may be formed. We consider this possibility and we describe, in the context of an effective lagrangian, the corresponding phonons as the Nambu-Goldstone bosons associated to the breaking of the space symmetries. (Contributed paper to the International Workshop SCGT 02 "Strong Coupling Gauge Theories and Effective Field Theories", 10-13 December 2002, Nagoya, Japan)
• K. Rajagopal, COLOUR SUPERCONDUCTIVITY. Published in *Beatenberg 2001, High-energy physics* 345-384
• T. Schafer, hep-ph/0304281. Quark Matter.
• R. Casalbuoni and G. Nardulli, hep-ph/0305069. Inhomogeneous Superconductivity in Condensed matter and QCD.
• D. H. Rischke, nucl-th/0305030. The Quark-Gluon Plasma in Equilibrium. Our current knowledge of the quark-gluon plasma in thermodynamical equilibrium is reviewed. The phase diagram of strongly interacting matter is discussed, with emphasis on the quark-hadron phase transition and the color-superconducting phases of quark matter. Lattice QCD results on the order of the phase transition, the thermodynamical functions, the heavy quark free energy, mesonic spectral functions, and recent results for nonzero quark chemical potential are presented. Analytic attempts to compute the thermodynamical properties of strongly interacting matter, such as perturbation theory, quasiparticle models, ``hard-thermal-loop''(HTL)-resummed perturbation theory, the Polyakov-loop model, as well as linear sigma models are discussed. Finally, color-superconducting quark matter is considered in the limit of weak coupling. The gap equation and the excitation spectrum are derived. The solution of the gap equation, gap parameters in various color-superconducting phases, and critical temperatures for the transition to normal-conducting quark matter are presented. A summary of gluon and photon properties in color superconductors is given. 
• J. A. Bowers, hep-ph/0305301. Color Superconducting Phases of Cold Dense Quark Matter. We investigate color superconducting phases of cold quark matter at densities relevant for the interiors of compact stars. At these densities, electrically neutral and weak-equilibrated quark matter can have unequal numbers of up, down, and strange quarks. The QCD interaction favors Cooper pairs that are antisymmetric in color and in flavor, and a crystalline color superconducting phase can occur which accommodates pairing between flavors with unequal number densities. In the crystalline color superconductor, quarks of different flavor form Cooper pairs with nonzero total momentum, yielding a condensate that varies in space like a sum of plane waves. Rotational and translational symmetry are spontaneously broken. We use a Ginzburg-Landau method to evaluate candidate crystal structures and predict that the favored structure is face-centered-cubic. We predict a robust crystalline phase with gaps comparable in magnitude to those of the color-flavor-locked phase that occurs when the flavor number densities are equal. Crystalline color superconductivity will be a generic feature of the QCD phase diagram, occurring wherever quark matter that is not color-flavor locked is to be found. If a very large flavor asymmetry forbids even the crystalline state, single-flavor pairing will occur; we investigate this and other spin-one color superconductors in a survey of generic color, flavor, and spin pairing channels. Our predictions for the crystalline phase may be tested in an ultracold gas of fermionic atoms, where a similar crystalline superfluid state can occur. If a layer of crystalline quark matter occurs inside of a compact star, it could pin rotational vortices, leading to observable pulsar glitches. Ph.D. thesis, submitted to the MIT Department of Physics, May 2003
  

• R. Casalbuoni and R. Gatto, hep-ph/9908227, Effective theory for color-flavor locking in high density QCD. The paper introduces the low-energy effective lagrangian for the CFL phase of QCD. (Phys.Lett. B464 (1999) 111-116)
• R. Casalbuoni and R. Gatto, hep-ph/9909419, The Color-Flavor Locking Phase at T \not =0$. Evaluation of the condensate at small temperatures. (Phys.Lett. B469 (1999) 213-219)
• R. Casalbuoni and R. Gatto, hep-ph/9911223, Pseudoscalar Masses in the Effective Theory for Color-Flavor Locking in high density QCD. A possible non-perturbative contribution to the masses of the NG bosons is exhibited (not published).
• R. Casalbuoni, Z. Duan and F. Sannino, hep-ph/0004207, Low Energy Theory for 2 flavors at High Density QCD. Construction of the effective lagrangian for the 2SC phase. (Phys.Rev. D62 (2000) 094004)
• R. Casalbuoni, R. Gatto and G. Nardulli, hep-ph/0010321, Dispersion Laws for In-medium Fermions and Gluons in the CFL Phase of QCD. Evaluation of the two-point function for gluons and NG bosons in the CFL phase, using the effective theory of frmions close to the Fermi surface. (Phys.Lett. B498 (2001) 179-188; Erratum-ibid. B517 (2001) 483)
• R. Casalbuoni, Z. Duan and F. Sannino, hep-ph/0011394, Electroweak Physics for Color Superconductivity. Effective theory for the 2SC and CFL phases including electro-weak interactions. (Phys.Rev. D63 (2001) 114026)
• R. Casalbuoni, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0101326, Effective Field Theory for the Crystalline Colour Superconductive Phase of QCD. Effective lagrangian for the LOFF phase. Anisotropic dispersion relation for the phonon. (Phys.Lett. B511 (2001) 218-228)
• R. Casalbuoni, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0107024, Effective gluon interactions in the Colour Superconductive Phase of two flavor QCD. Evaluation of the two- three- and four- point functions of the gluons in the 2SC phase. (Phys.Lett. B524 (2002) 144-152)
• R. Casalbuoni, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0201059, Anisotropy Parameters for the Effective Description of Crystalline Color Superconductors. The parameters of the effective lagrangian describing the LOFF phase are evaluated. (Phys.Rev. D66 (2002) 014006)
• R. Casalbuoni, R. Gatto and G. Nardulli, hep-ph/0205219, Crystalline Color Superconductivity: Effective Lagrangian and Phonon Dispersion Law. Effective lagrangian for the cubic crystalline phase of QCD. (Phys. Lett. B543 (2002) 139)
• R. Casalbuoni, E. Fabiano, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0208121. Phonons and gluons in the crystalline color superconducting phase of QCD.The High Density Effective Theory formalism is used to calculate the low energy properties of the phonons and gluons in the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of two-flavor QCD. Calculations are done for the phonons of the cubic crystal and of the gluons for the cube and for the single plane wave. 
• R. Casalbuoni, F. De Fazio, R. Gatto, G. Nardulli and M.Ruggieri, hep-ph/0209105. Massive quark effects in two flavor color superconductors. The high density effective theory formalism (HDET) is employed to describe high density QCD with  two massive flavors (2SC).  The gap equation is derived and explicitly solved for the gap parameter. The parameters associated to the pseudo Nambu-Goldstone boson of $U(1)_A$ are evaluated in the limit $\mu\to\infty$ and$m/\mu$ fixed.
• R. Casalbuoni, R. Gatto, G. Nardulli, M. Ruggieri, hep-ph/0302077. Aspects of the Color Flavor Locking phase of QCD in the Nambu-Jona Lasinio approximation. We study two aspects of the CFL phase of QCD in the NJL approximation. The first one is the issue of the dependence on \mu of the ultraviolet cutoff in the gap equation, which is solved allowing a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using the high density effective theory we perform an expansion in the parameter (m_s/\mu)^2 after checking that its numerical validity is very good already at first order.
  

• M. G. Alford, K. Rajagopal and F. Wilczek, hep-ph/9802284. Color superconductivity and sign of its formation. Suggestions that the formation of  a color superconducting condensate  in a heavy ion collision may be accompanied by radiation of negative pions, and its decay may yield more protons than were present in the incident nuclei. (Nucl.Phys. A638 (1998) 515c-518c)
• K. Rajagopal, hep-ph/9803341. QCD at finite baryon density: chiral symmetry restoration and color superconductivity. Review of hep-ph/9711395. (Prog.Theor.Phys.Suppl. 131 (1998) 619-631)
• K. Rajagopal, hep-ph/9807318. Three flavor QCD at high density: color flavor locking and chiral symmetry breaking. A symmetry breaking scheme is proposed for QCD with three massless quarks at high baryon density wherein the color and flavor     SU(3)_{color}xSU(3)_{L}xSU(3)_{R} symmetries are broken down to the diagonal subgroup SU(3)_{color+L+R} by the formation of a condensate of quark Cooper pairs. (Nucl.Phys. A642 (1998) 26-38)
• K. Rajagopal, hep-ph/9808348, The QCD tricritical point: beyond monotony in heavy ion physics. Tricritical point in QCD and superconducting phases. (Talk given at 3rd Workshop on Continuous Advances in QCD (QCD 98), Minneapolis, MN, 16-19 Apr 1998.)
• K. Rajagopal, hep-ph/9908360. Mapping the QCD phase diagram. Tricritical point and high density QCD. (Nucl.Phys.A661:150-161,1999)
• Deog Ki Hong, hep-ph/0003215. Color Superconductivity in High Density Effective Theory. In this talk, I discuss the recent development in color superconductivity in terms of effective field theory. By investigating the Cooper pair gap equations at high density, we see that the effective theory simplifies the gap analysis very much, especially in finding the ground state, the precise form of the gap, and the critical     temperature. (contribution to TMU-Yale Symposium on Dynamics of Gauge Fields)
• K. Rajagopal, hep-ph/0009058. The phases of QCD in heavy ion collisions and compact stars. Review of the arguments for the existence of a critical point in the QCD phase diagram as a function of temperature and baryon chemical potential and of the    phenomena expected in cold dense quark matter: color superconductivity andcolor-flavor locking. (7th Conference on Intersections Between Particle and Nuclear Physics (CIPANP 2000), Quebec City, Quebec, Canada, 22-28 May 2000, and of 40th Jubilee Cracow School of Theoretical Physics: Quantum Phase Transitions in High Energy and Condensed Matter Physics, Zakopane, Poland, 3-11 Jun 2000. Published in Acta Phys.Polon.B31:3021,2000)
• M. G. Alford, J. A. Bowers and K. Rajagopal, hep-ph/0009357. Color superconductivity in compact stars. Some implications of recent developments in our understanding of cold dense quark matter for the physics of compact stars. (Strong and Electroweak Matter 2000, Marseille, France, June 2000. Strangeness 2000, Berkeley, CA, July 2000. ECT International Workshop on Physics of Neutron Star Interiors (NSI00), Trento, Italy, 19 Jun - 7 Jul 2000. Published in J.Phys.G27:541-556,2001, Lect.Notes Phys.578:235-252,2001 Also in *Trento 2000, Physics of neutron star interiors 235-252)
• R. Casalbuoni, hep-th/0108195, Effective lagrangians for QCD at high density. A review of CFL and LOFF phases (Martina Franca 2001, QCD@WORK).
• K. Rajagopal, hep-ph/0109135, Crystalline color superconductivity. Review of the LOFF phase (AIP Conf.Proc.602:339-351,2001, Nucl.Phys.A702:25-38,2002, Martina Franca 2001, QCD@WORK)
• S.D.H. Hsu, hep-ph/0111049. The QCD Phase Diagram and Explosive Astrophysics. I give a brief overview of our current understanding of the QCD phase diagram at finite temperature and baryon density. I emphasize phase transitions which occur at high density and low temperature (relative to the QCD scale), such as transition(s) to the color superconducting and chirally symmetric phases. These transitions might occur during violent astrophysical activity such as type II supernovae core bounce or neutron star mergers, and I discuss the possible consequences. (eConf C010815 (2002) 64-75)
• R. Casalbuoni, hep-ph/0110107, Effective description of QCD at high density. Review of CFL and of the evaluation of the parameters for the NG bosons and gluons (Copenhagen 2001, eConf C010815: 88-103, 2002)
• G. Nardulli,hep-ph/0111178, Effective theory for QCD in the LOFF phase. Review of the LOFF phase (Copenhagen 2001, eConf C010815:104-109, 2002)
• D.K. Hong, hep-ph/0112028. Crystalline Color Superconductivity in Dense Matter. In this talk I discuss a recently proposed color superconducting phase of asymmetric quark matter where the up and down quark have different chemical potential, being in chemical equilibrium with electrons. Using Schwinger-Dyson equations derived from an effective theory of low-energy quasiparticles, a critical     coupling for LOFF phase is estimated for both the case of an effective four Fermi interaction and Landau-damped one gluon exchange. (eConf C010815 (2002) 116-124)
• T. Schaefer, nucl-th/0201031. Superdense Matter. We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density. (talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001)
• F. Sannino, hep-ph/0205007. Aspects of the Quantum Chromo Dynamics Phase Diagram. I briefly review some aspects of the Quantum Chromo Dynamics phase diagram at non zero temperature and quark chemical potential. I then suggest new possible phases which can appear in strongly interacting theories at non zero chemical potential. Finally I describe the phase diagram as function of the number of flavors and colors at zero quark chemical potential and zero temperature. (Invited review talk for the GISELDA Meeting held in Frascati, 14-18 January 2002)
• M.Mannarelli, hep-ph/0205098.Effective description of the LOFF phase of QCD. We present an effective field theory for the crystalline color superconductivity phase of QCD. It is kown that at high density and at low temperature QCD exhibits  a transition to a color superconducting phase characterized by energy gaps in the fermion spectra. Under specific circumstances the gap parameter has a crystalline pattern, breaking translational and rotational invariance.(Talk at the Giselda Meeting, Frascti (Roma), 14-18 Jan 2001
• G. Nardulli,hep-ph/0206065, Effective fields in dense quantum cromodynamics. Review of LOFF phase and discussion about vortices and glitches (Frascati 2002)
• Compact stars in the QCD phase diagram. Conference at NORDITA, August 2001.
• T. Schaefer, nucl-th/0208070. Effective Theory of the Color-Flavor-Locked Phase. We explain how an effective theory of the CFL phase can be used to study the effect of the strange quark mass on the ground state and the excitation spectrum. We also apply the effective theory to the problem of neutrino emission from a CFL quark core inside a neutron star.
• J.A. Bowers, K. Rajagopal, hep-ph/0209168. The crystallography of color superconductivity. We describe the crystalline phase of color superconducting quark matter. This phase may occur in quark matter at densities relevant for compact star physics, with possible implications for glitch phenomena in pulsars. We use a Ginzburg-Landau approach to determine that the crystal has a face-centered-cubic (FCC) structure. Moreover, our results indicate that the phase is robust, with gaps, critical temperature, and free energy comparable to those of the color-flavor-locked (CFL) phase. Our calculations also predict ``crystalline superfluidity'' in ultracold gases of fermionic atoms. (Quark Matter 2002, Nantes, France)
• M.G. Alford, hep-ph/0209287. QCD at high density/temperature. I give a survey of recent progress in our understanding of QCD at high density and temperature. I pay particular attention to color superconductivity, applications of lattice gauge theory at nonzero density as well as high temperature, perturbative results at high temperature, and non-equilibrium calculations. (ICHEP 2002 plenary review talk)
  

• M. G. Alford, K. Rajagopal and F. Wilczek, hep-ph/9711395. QCD at finite baryon density: nucleon droplets and color superconductivity. A study of finite density QCD in an approximation in which the interaction between quarks is modelled by that induced by  instantons.  At all densities high enough tit is found  that color symmetry is broken by the formation of a <qq> condensate of quark Cooper pairs. (Phys.Lett. B422 (1998) 247-256)
• M. G. Alford, K. Rajagopal and F. Wilczek, hep-ph/9804403. Color flavor locking and chiral symmetry breaking in high density QCD. A symmetry breaking scheme for QCD is proposed with three massless quarks at high baryon density wherein the color and flavor SU(3)_color times SU(3)_L  times SU(3)_R symmetries are broken down to the diagonal subgroup SU(3)_{color+L+R} by the formation of a condensate of quark Cooper pairs. Discussion of NGB's  and modified QED. (Nucl.Phys. B537 (1999) 443-458)
• M. G. Alford, J. Berges and K. Rajagopal, hep-ph/9908235. Gapless color superconductivity. Derivation of the dispersion relations for quasiparticle excitations about the color-flavor locked ground state of QCD at    high baryon density. In the presence of condensates which pair light and strange quarks there need not be an energy gap in the quasiparticle spectrum. (Phys.Rev.Lett.84:598-601,2000)
• M. G. Alford, J. Berges and K. Rajagopal, hep-ph/9910254. Magnetic fields within color superconducting neutron star cores. Discussion of  the Meissner effect for a color superconductor formed by cold dense quark matter. (Nucl.Phys.B571:269-284,2000)
• K. Rajagopal, E. Shuster, hep-ph/0004074. On the applicability of weak coupling results in high density QCD. It is shown that  present weak-coupling calculations of Delta  can only be trusted for mu >> mu_c ~ 10^8 MeV. (Phys.Rev.D62:085007,2000)
• M. G. Alford, J. A. Bowers and K. Rajagopal, hep-ph/0008208. Crystalline color superconductivity. In the case of pairing between species of    quarks with differing chemical potentials, for suitable values of the differences between chemical potentials, Cooper pairs with nonzero total momentum are favored, as was first realized by Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort spontaneously break translational and rotational invariance, leading to gaps which vary periodically in a crystalline pattern. (Phys.Rev.D63:074016,2001)
• K. Rajagopal and F. Wilczek, hep-ph/0012039. Enforced electrical neutrality of the color flavor locked phase. It is shown that quark matter in the CFL phase of QCD is rigorously electrically neutral, despite  the unequal quark masses, and even in the presence of an electron chemical potential.  (Phys.Rev.Lett.86:3492-3495,2001)
• J. A. Bowers, J. Kundu, K. Rajagopal and E. Shuster, hep-ph/0101067. A Diagrammatic approach to crystalline color superconductivity. Derivation of the gap equation through the Schwinger-Dyson equation and Nambu-Gorkov propagator. (Phys.Rev. D64 (2001) 014024)
• A. K. Leibovich, K. Rajagopal and E. Shuster, hep-ph/0104073. Opening the crystalline color superconductivity window. The window for the LOFF phase is re-evaluated using one-gluon exchange interaction. (Phys.Rev. D64 (2001) 094005)
• M. Alford, K. Rajagopal, S. Reddy and F. Wilczek, hep-0105009. The minimal CFL nuclear interface. The interface betwwen CFL and nuclear phase is studied. (Phys.Rev.D64:074017,2001)
• C. Manuel and  K. Rajagopal, hep-ph/0107211.Illuminating dense quark matter. Evaluation of angles of reflections and rifractions for light illuminating a lump of cold dense quark matter. (Phys.Rev.Lett.88:042003,2002 )
• J. Kundu  and, K. Rajagopal, hep-ph/0112206.Mass induced crystalline color superconductivity. The LOFF phase is obtained by allowing a quark with non zero mass. (Phys.Rev.D65:094022,2002)
• M. Alford and K. Rajagopal, hep-ph/0204001.Absence of two flavor color superconductivity in compact stars. Evidence for absence of the 2SC phase in favor of CFL and/or LOFF phase
• J. A. Bowers and K. Rajagopal, hep-ph/0204079.The crystallography of color superconductivity.Calculation of the crystalline structure minimizing the free energy in the LOFF phase
• A. Gerhold, A. Rebhan, hep-ph/0305108. Gauge dependence identities for color superconducting QCD. Using generalized Nielsen identities a formal proof is given that the fermionic quasiparticle dispersion relations in a color superconductor are gauge independent. This turns out to involve gluonic tadpoles which are calculated to one-loop order in a two-flavor color superconductor. Regarding the appearance of gluon tadpoles, we argue that in QCD the color superconducting phase is automatically color neutral. 
• I. Giannakis, Hai-cang Ren, hep-ph/0305235. The Ginzburg-Landau Theory and the Surface Energy of a Colour Superconductor. We apply the Ginzburg-Landau theory to the colour superconducting phase of a lump of dense quark matter. We calculate the surface energy of a domain wall separating the normal phase from the super phase with the bulk equilibrium maintained by a critical external magnetic field. Because of the symmetry of the problem, we are able to simplify the Ginzburg-Landau equations and express them in terms of two components of the di-quark condensate and one component of the gauge potential. The equations also contain two dimensionless parameters: the Ginzburg-Landau parameter ${\kappa}$ and ${\rho}$. The main result of this paper is a set of inequalities obeyed by the critical value of the Ginzburg-Landau parameter--the value of ${\kappa}$ for which the surface energy changes sign--and its derivative with respect to ${\rho}$. In addition we prove a number of inequalities of the functional dependence of the surface energy on the parameters of the problem and obtain a numerical solution of the Ginzburg-Landau equations. Finally a criterion for the types of colour superconductivity (type I or type II) is established in the weak coupling approximation. 
• D. K. Hong and S.D.H. Hsu, hep-ph/0304156. Positivity and Dense Matter. We elaborate on previous results concerning the positivity of the Euclidean path integral measure for low-energy modes in dense fermionic matter. We show that the sign problem usually associated with fermions is absent if one considers only low-energy degrees of freedom. We describe a method for simulating dense QCD on the lattice and give a proof using rigorous inequalities that the color-flavor locked (CFL) phase is the true vacuum of three flavor, massless QCD. We also discuss applications to electronic systems in condensed matter, such as generalized Hubbard models.
  

• C. Manuel, hep-ph/9512365. Hard Dense Loops in a Cold Non-Abelian Plasma. Classical transport theory is used to study the response of a non-Abelian plasma at zero temperature and high chemical potential to weak color electromagnetic fields. In this article the parallelism between the transport phenomena occurring in a non-Abelian plasma at high temperature and high density is stressed. (Phys.Rev. D53 (1996) 5866-5873)
• Robert D. Pisarski, Michel Tytgat, hep-ph/9604404. Propagation of Cool Pions. For an exact chiral symmetry which is spontaneously broken at zero temperature, we show that at nonzero temperature, generally pions travel at  less than the speed of light.
• R. Rapp, T. Schafer, E.V. Shuryak and M. Velkovsky, hep-ph/9711396. Diquark bose condensates in high density matter and instantons. Study of the non perturbative effects on the gap Phys.Rev.Lett.81:53-56,1998
• J. Berges and K. Rajagopal, hep-ph/9804233.Color Superconductivity and Chiral Symmetry Restoration at Nonzero Baryon Density and Temperature. Exploration of the phase diagram of strongly interacting matter as a function of temperature and baryon number density, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons. (Nucl. Phys. B538, 215 (1999))
• N. Evans, S. D. H. Hsu and M. Schwetz, hep-ph/9808444.An Effective Field Theory Approach to Color Superconductivity at High Quark Density. Investigation of the Fermi Liquid theory of high density QCD. Using the renormalization group (RG), we determine the behavior of effective fermion interactions near the Fermi surface. (Nucl. Phys. B551, 275 (1999))
• T. Schafer and F. Wilczek, hep-ph/9810509.High Density Quark Matter and the Renormalization Group in QCD with two and three flavors. We consider the most general four fermion operators in QCD for two and three massless flavors and study their renormalization in the vicinity of the Fermi surface. (Phys. Lett. B450, 325 (1999))
• N. Evans, S. D. H. Hsu and M. Schwetz, hep-ph/9810514.Non-Perturbative Couplings and Color Superconductivity. We study the     renormalization group flow to the Fermi surface of the full set of couplings generated by gluonic and instanton interactions. (Phys. Lett. B449, 281 (1999))
• R. D. Pisarski and D. H. Rischke, nucl-th/9811104.A first order transition and parity violation in a color superconductor. At densities sufficiently high to (effectively) restore the axial U(1) symmetry, then relative to the ordinary vacuum, the condensation of up with down quarks (effectively) breaks parity spontaneously. Phys. Rev. Lett. 83, 37 (1999)
• Kurt Langfeld, Mannque Rho, hep-ph/9811227. Quark Condensation, Induced Symmetry Breaking and Color Superconductivity at High Density. The phase structure of hadronic matter at high density relevant to the physics of compact stars and relativistic heavy-ion collisions is studied in a low-energy effective quark theory. The relevant phases that figure are (1) chiral condensation, (2) diquark color condensation (color superconductivity) and (3) induced Lorentz-symmetry breaking (ISB). (Nucl. Phys. A660 (1999) 475-505)
• J. Berges, D.-U. Jungnickel, C. Wetterich, hep-ph/9811387. Quark and Nuclear Matter in the Linear Chiral Meson Model. The equation of state for quark and nuclear matter is encoded in the effective potential of a linear sigma model. We exploit an exact differential equation for its dependence upon the chemical potential associated to conserved baryon number.
• T. Schafer and F. Wilczek, hep- ph/9811473. Continuity of Quark and Hadron Matter.  We present evidence that for three degenerate flavors the qualitative features of the color-flavor locked state, reliably predicted for high density, match the expected features of hadronic matter at low density. (Phys. Rev. Lett. 82, 3956 (1999))
• D. T. Son, hep-ph/9812287. Superconductivity by long-range color magnetic interaction in high-density quark matter.We argue that in quark matter at high densities, the color magnetic field remains unscreened and leads to the phenomenon of color superconductivity. (Phys. Rev. D59, 094019 (1999))
• G. W. Carter and D. Diakonov, hep-ph/9812445.Light Quarks in the Instanton Vacuum at Finite Baryon Density. Since the instanton-induced interactions are attractive in both $\bar{q}q$ and $qq$ channels, a competition ensues between phases of matter with condensation in either or both. It results in chiral symmetry restoration due to the onset of diquark condensation, a `colour supercondutor', at finite density. (Phys. Rev. D60, 016004 (1999))
• D.K. Hong, hep-ph/9812510. An effective field theory of QCD at high density. We derive a (Wilsonian) effective field theory of QCD at finite density by integrating out the states in the Dirac sea when the chemical potential$\mu\gg\Lambda_{\rm QCD}$. The quark-gluoncoupling is effectively (1+1)-dimensional and the theory contains four-quark operators which become relevant  as we approach to the Fermi sea. (Phys. Lett. B473, 118 (2000))
• J. Hosek, hep-ph/9812516. Macroscopic quantum phases of a deconfined QCD matter at finite density. Formalism for a unified description of distinct superfluid phases of a deconfined QCD matter at finite density together with the phase of spontaneously broken chiral symmetry is presented. Dispersion laws of the quasiquark excitations in both diamagnetic and ferromagnetic phases with spontaneously broken chiral symmetry are exhibited explicitly.
• UKQCD Collaboration, Phys. Rev. D59 (1999) 116002.
• S. Hands, J. B. Kogut, M. Lombardo and S. E. Morrison, hep-lat/9902034. Symmetries and spectrum of SU(2) Lattice Gauge Theory at finite chemical potential. We study SU(2) Lattice Gauge Theory with dynamical fermions at non-zero chemical potential $\mu$. The symmetries special to SU(2) for staggered fermions on the lattice are discussed explicitly and their relevance to spectroscopy and condensates at non-zero chemical potential are considered.(Nucl. Phys. B558, 327 (1999))
• S. Chandrasekharan and U. Wiese, cond-mat/9902128. Meron-Cluster Solution of Fermion Sign Problems. We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. (Phys. Rev. Lett. 83, 3116 (1999)
• N. O. Agasian, B. O. Kerbikov and V. I. Shevchenko, hep-ph/9902335.Nonperturbative QCD vacuum and Colour superconductivity. We argue, that nonperturbative gluonic fields might play a crucial role in colour superconductivity scenario. (Phys. Rept. 320, 131 (1999))
• R. D. Pisarski and D. H. Rischke, nucl-th/9903023. Superfluidity in a Model of Massless Fermions Coupled to Scalar Bosons. We study superfluidity in a model of massless fermions coupled to a massive scalar field through a Yukawa interaction.(Phys. Rev. D60, 094013 (1999))
• T.M. Schwarz, S.P. Klevansky and G. Papp, nucl-th/9903048. The phase diagram and bulk thermodynamical quantities in the NJL model at finite temperature and density. Comparison of the instanton model and NJL at finite temperature and density. (Phys.Rev. C60 (1999) 055205)

M. Alford, J. Berges and K. Rajagopal, hep-ph/9903502. Unlocking Color and Flavor in Superconducting Strange Quark Matter. We explore the phase diagram of strongly interacting matter with massless u and d quarks as a function of the strange quark mass m_s and the chemical potential mu for baryon number. As the density is reduced, for sufficiently large m_s we observe a first order transition from the color-flavor locked phase to a color superconducting phase analogous to that in two flavor QCD. (Nucl. Phys. B558, 219 (1999))
• T. Schafer and F. Wilczek, hep-ph/9903503.Quark Description of Hadronic Phases.  We extend our proposal that major universality classes of hadronic matter can be understood, and in favorable cases calculated, directly in the microscopic quark variables, to allow for splitting between strange and light quark masses. A surprisingly simple but apparently viable picture emerges, featuring essentially three phases, distinguished by whether strangeness is conserved (standard nuclear matter), conserved modulo two (hypernuclear matter), or locked to color (color flavor locking). These are separated by sharp phase transitions. There is also, potentially, a quark phase matching hadronic K-condensation. (Phys. Rev. D60, 074014 (1999))
• R. Rapp, T. Schafer, E. V. Shuryak and M. Velkovsky, hep-ph/9904353.High Density QCD and Instantons.  Instantons generate strong non-perturbative interactions between quarks. In the vacuum, these interactions lead to chiral symmetry breaking and generate constituent quark masses on the order of 300-400 MeV. The observation that the same forces also provide attraction in the scalar diquark channel leads to the prediction that cold quark matter is a color superconductor, with gaps as large as $\sim$~100 MeV.(Ann als Phys. 280, 35 (2000)
• I.J.R. Aitchison, D.J. Lee and G. Metikas, cond-mat/9905008. Finite Temperature Time-Dependent Effective Theory For The Goldstone Field In A BCS-Type Superfluid. We extend to finite temperature the time-dependent effective theory for the Goldstone field (the phase of the pair field) $ \theta $ which is appropriate for a superfluid containing one species of fermions with s-wave interactions, described by the BCS Lagrangian.
• J. B. Kogut, M. A. Stephanov and D. Toublan, hep-ph/9906346. On two-color QCD with baryon chemical potential. We study SU(2) color QCD with even number of quark flavors. First, using QCD inequalities we show that at finite baryon chemical potential mu, condensation     must occur in the channel with scalar diquark quantum numbers. (Phys. Lett. B464, 183 (1999))
• G.W. Carter and D. Diakonov, hep-ph/9905465. Chiral Symmetry Breaking and Color Superconductivity in the Instanton Picture. The instanton approach to spontaneous chiral symmetry breaking is reviewed, with emphasis on the connection to chiral random matrix theory.
• E. Shuster and D. T. Son, hep-ph/9905448. On finite-density QCD at large Nc. Deryagin, Grigoriev, and Rubakov (DGR) have shown that in finite-density QCD at infinite Nc the Fermi surface is unstable with respect to the formation of chiral waves with wavenumber twice the Fermi momentum, while the BCS instability is suppressed. We show here that at large, but finite Nc, the DGR instability only occurs in a finite window of chemical potentials from above Lambda_QCD to mu_critical = exp(gamma ln^2 Nc + O(ln Nc ln ln Nc))Lambda_QCD, where gamma = 0.02173. Our analysis shows that, at least in the perturbative regime, the instability occurs only at extremely large Nc, Nc > 1000 Nf, where Nf is the number of flavors. We conclude that the DGR instability is not likely to occur in QCD with three colors, where the ground state is expected to be a color superconductor. (Nucl. Phys. B573, 434 (2000))
• D. K. Hong, hep-ph/9905523.Aspects of high density effective theory in QCD. We investigate the Cooper pair gap equation and find that the color-flavor locking phase is energetically preferred at high density. We also find the color-superconducting phase transition occurs in dense quark matter when the chemical potential is larger than $250\pm 100~{\rm MeV}$ and the temperature is lower than 0.57 times the Cooper pair gap in the leading order in the hard-dense-loop approximation. (Nucl. Phys. B582, 451 (2000))
• D. K. Hong, V. A. Miransky, I. A. Shovkovy and L. C. Wijewardhana, hep-ph/9906478.Schwinger-Dyson Approach to Color Superconductivity in Dense QCD. The problem of color superconductivity in dense QCD is reconsidered in the improved rainbow approximation to the Schwinger-Dyson equation. The effect of the unscreened magnetic modes of gluons on the value of the color condensate is studied. In particular, it is shown that, at sufficiently large values of the chemical potential, these modes lead to the enhancement of the superconducting order parameter.(Phys. Rev. D61, 056001 (2000), erratum ibid. D62, 059903 (2000))
• T. Schafer and F. Wilczek, hep-ph/9906512.Superconductivity from perturbative one-gluon exchange in high density quark matter. We study color superconductivity in QCD at asymptotically large chemical potential. In this limit, pairing is dominated by perturbative one-gluon exchange. We derive the Eliashberg equation for the pairing gap and solve this equation numerically. Taking into account both magnetic and electric gluon exchanges, we find $\Delta\sim g^{-5}\exp(-c/g)$ with $c=3\pi^2/\sqrt{2}$, verifying a recent result by Son. For chemical potentials that are of physical interest, $\mu< 1$ GeV, the calculation ceases to be reliable quantitatively, but our results suggest that the gap can be as large as 100 MeV. (Phys. Rev. D60, 114033 (1999))
• D. K. Hong, M. Rho and I. Zahed, hep-ph/9906551.Qualitons At High Density. In the color-flavor-locked (CFL) phase of the QCD superconductor we show that baryons behave as qualitons (called "superqualitons") with quantum numbers $B=(1{\rm mod} 2)/3$, S=1/2 and Y=B. (Phys. Lett. B468, 261 (1999))
• R. D. Pisarski and D. H. Rischke, nucl-th/9907041.Gaps and Critical Temperature for Color Superconductivity.  Because of a logarithmic enhancement from soft, collinear magnetic gluons, in dense quark matter the gap for a color superconducting condensate with spin zero depends upon the QCD coupling constant g not as exp(-1/g^2), like in BCS theory, but as exp(-1/g). (Phys. Rev. D61, 051501 (2000))
• J. Meyer, G. Papp, H.-J. Pirner and T. Kunihiro, nucl-th/9908019. Renormalization Group Flow Equation at Finite Density. For the linear sigma model with quarks we derive renormalization group flow equations for finite temperature and finite baryon density using the heat kernel cutoff. (Phys.Rev. C61 (2000) 035202)
• W. E. Brown, J. T. Liu and H. Ren, hep-ph/9908248.On the Perturbative Nature of Color Superconductivity. We present a systematic derivation of the transition temperature, T_C, from the QCD Lagrangian through study of the di-quark proper vertex. (Phys. Rev. D61, 114012 (2000))
• S.D.H. Hsu and M. Schwetz, hep-ph/9908310. Magnetic interactions, the renormalization group and color superconductivity in high density QCD. Investigation of the effects of long range magnetic interactions on the RG evolution of local Cooper pairing interactions near the Fermi surface in high density QCD
• F. Wilczek, hep-ph/9908480. The recent excitement in high-density QCD. Review of high-density QCD.
• A. Chodos, F. Cooper, W. Mao, H. Minakata and A. Singh, hep-ph/9909296. A two-dimensional model with chiral condensates and Coopre pairs having QCD-like phase structure. Study of superconducting phases in a two-dimensional model
• T. Schafer,  hep-ph/9909574.Patterns of Symmetry Breaking in QCD at High Baryon Density.  We study the structure of QCD at very large baryon density for an arbitrary number of flavors $N_f$. (Nucl. Phys. B575, 269 (2000))
• R. D. Pisarski and D. H. Rischke, nucl-th/9910056.Color superconductivity in weak coupling. We derive perturbatively the gap equations for a color-superconducting condensate with total spin J=0 in dense QCD. At zero temperature, we confirm the results of Son for the dependence of the condensate on the coupling constant, and compute the prefactor to leading logarithmic accuracy. (Phys.Rev. D61, 074017 (2000))
• I. A. Shovkovy and L. C. Wijewardhana, hep-ph/9910225.On gap equations and color-flavor locking in cold dense QCD with three massless flavors. The superconductivity in cold dense QCD with three massless flavors is analyzed in the framework of the Schwinger-Dyson equation. The set of two coupled gap equations for the color antitriplet, flavor antitriplet (bar{3},bar{3}) and the color sextet, flavor sextet (6,6) order parameters is derived. It is shown that the antitriplet-antitriplet gives the dominant contribution to the color-flavor locked order parameter, while the sextet-sextet is small but nonzero. (Phys. Lett. B470, 189 (1999))
• N. Evans, J. Hormuzdiar, S. D. Hsu and M. Schwetz,  hep-ph/9910313.On the QCD Ground State at High Density. We show that, as previously anticipated, in the two flavor case the vacuum breaks SU(3) color to SU(2) and in the three flavor case the vacua with  color-flavor locking (CFL) have the lowest energy. We identify a number of relatively flat directions in the potential along which the pattern of gauge symmetry breaking changes and parity is violated. We discuss possible phenomenological consequences of our results. (Nucl. Phys. B581,391 (2000))
• B. Park, M. Rho, A. Wirzba and I. Zahed, hep-ph/9910347.Dense QCD : Overhauser or BCS Pairing ? We discuss the Overhauser effect (particle-hole pairing) versus the BCS effect (particle-particle or hole-hole pairing) in QCD at large quark density. In weak coupling and to leading logarithm accuracy, the pairing energies can be estimated exactly. For a small number of colors, the BCS effect overtakes the Overhauser effect, while for a large number of colors the opposite takes place, in agreement with a recent renormalization group argument.(Phys. Rev. D62, 034015 (2000))
• D. T. Son and M. A. Stephanov, hep-ph/9910491.Inverse meson mass ordering in color-flavor-locking phase of high density QCD. We derive the effective Lagrangian for the low-energy massive meson excitations of the color-flavor-locking (CFL) phase of QCD with 3 flavors of light quarks. We compute the decay constants, the maximum velocities, and the masses of the mesons at large baryon chemical potential mu.(Phys. Rev. D61, 074012 (2000); erratum, ibid. D62, 059902 (2000), hep-ph/0004095.)
• M. Rho, A. Wirzba and I. Zahed, hep-ph/9910550. Generalized Pions in Dense QCD. QCD superconductors in the color-flavor-locked (CFL) phase sustain light Goldstone modes (that will be referred to as generalized pions) that can be described as pairs of particle and/or hole excitations around a gapped Fermi surface. (Phys. Lett. B473, 126 (2000))
• E.V. Shuryak, hep-ph/9911244. Scales and Phases of Non-Perturbative QCD. The covered topic include (i) discussion of the scales at which perturbative description should be changed by the non-perturbative one. A number of various examples are considered, leading to different scales, related to instantons or confinement effects; (ii) Instanton vacuum as an Instanton Liquid; (iii) The phase diagram of QCD at finite temperature and density, and especially description of a recent progress in Color Superconductivity. (lectures at UK Theory Institute, Swansea UK, Sept.99; and XVII School ``QCD: Perturbative or Non-perturbative?'' Lisbon, Portugal, Oct.99)
• E.B. Gregory, S. Guo, H. Kroger, Xiang-Qian Luo, hep-lat/9912054. Hamiltonian lattice QCD at finite chemical potential. At sufficiently high temperature and density, quantum chromodynamics (QCD) is expected to undergo a phase transition from the confined phase to the quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo method works well for QCD at finite temperature, however, it breaks down at finite chemical potential. We develop a Hamiltonian approach to lattice QCD at finite chemical potential and solve it in the case of free quarks and in the strong coupling limit. (Phys. Rev. D62 (2000) 054508)
• W. E. Brown, J. T. Liu and H. Ren, hep-ph/9912409.The Transition Temperature to the Superconducting Phase of QCD at High Baryon Density. Based on the dominant one-gluon-exchange interaction, both the transition temperature and zero temperature gap have been determined to leading order in the coupling, g. While the leading non-BCS behavior, $T_C\sim\mu g^{-5}e^{-\kappa/g}$, is easily obtained, the pre-exponential factor has proved more difficult to evaluate. Focusing on the transition temperature, we present a perturbative derivation of this factor, exact to leading order in g. (Phys. Rev. D62, 054016 (2000))
• H. Heiselberg, hep-ph/9912419. Color superconducting quark matter in neutron stars. Color superconductivity in quark matter is studied for electrically charge neutral neutron star matter in b-equilibrium.
• D. K. Hong, T. Lee and D. Min, hep-ph/9912531. Meson Mass at Large Baryon Chemical Potential in Dense QCD.We reexamine the quark mass induced term in chiral Lagrangian in color-flavor locking phase in dense QCD, and show that the meson mass term is determined by three independent invariants under chiral-axial symmetry. (Phys. Lett. B477, 137 (2000))
• D. H. Rischke, nucl-th/0001040.Debye screening and Meissner effect in a two-flavor color superconductor. I compute the gluon self-energy in a color superconductor with two flavors of massless quarks, where condensation of Cooper pairs breaks SU(3)_c to SU(2)_c. (Phys. Rev. D62, 034007 (2000))
• C. Manuel and M. H. Tytgat, hep-ph/0001095.Masses of the Goldstone modes in the CFL phase of QCD at finite density. We construct the U_L(3) x U_R(3) effective lagrangian which encodes the dynamics of the low energy pseudoscalar excitations in the color-Flavor-Locking superconducting phase of QCD at finite quark density. We include the effects of instanton-induced interactions and study the mass pattern of the pseudoscalar mesons. A tentative comparison with the analytical estimate for the gap suggests that some of these low energy momentum modes are not stable for moderate values of the quark chemical potential.(Phys. Lett. B479, 190 (2000))
• M. Rho, E. Shuryak, A. Wirzba and I. Zahed, hep-ph/0001104.Generalized Mesons in Dense QCD. QCD superconductors in the color-flavor-locked (CFL) phase support excitations (generalized mesons) that can be described as pairs of particles or holes (rather than particle-hole) around a gapped Fermi surface.(Nucl. Phys. A676, 273(2000))
• O. Kiriyama, M. Maruyama and F. Takagi, hep-ph/0001108. Chiral phase transition at high temperature and density in the QCD-like theory. The chiral phase transition at finite temperature T and/or chemical potential $\mu$ is studied using the QCD-like theory with a variational approach. The  ``QCD-like theory'' means the improved ladder approximation with an infrared cutoff in terms of a modified running coupling. The form of Cornwall-Jackiw-Tomboulis effective potential is modified by the use of the Schwinger-Dyson equation for generally nonzero current quark mass. (Phys.Rev. D62 (2000) 105008)
• J.B. Kogut, M.A. Stephanov, D. Toublan, J.J.M. Verbaarschot, A. Zhitnitsky, hep-ph/0001171. QCD-like Theories at Finite Baryon Density. We study QCD-like theories with pseudoreal fermions at finite baryon density. Such theories include two-color QCD with quarks in the fundamental     representation of the color group as well as any-color QCD with quarks in the adjoint color representation. (Nucl.Phys. B582 (2000) 477-513)
• G. Carter and D. Diakonov, hep-ph/0001318.The Nonperturbative Color Meissner Effect in a Two-Flavor Color Superconductor. In order to analyze this effect at low quark density, when gaps are large and generated nonperturbatively, we use instanton-induced quark interactions augmented with gauge-invariant interactions between quarks and perturbative gluons. The five gluon masses are found from the static limit of the relevant polarization operators, in which transversality is maintained via the Nambu-Goldstone modes of broken color symmetry. Working in the microscopic theory we calculate these masses to one-loop order and estimate their density dependence.(Nucl. Phys. B582, 571 (2000))
• K. Zarembo, hep-ph/0002123. Dispersion Laws for Goldstone Bosons in a Color Superconductor.  The effective action valid at energies and momenta comparable to the gap is derived. Dispersion laws following from this action are such that the energy of Goldstone bosons is always smaller than the gap in the quasiparticle spectrum, and Goldstone bosons always propagate without damping. (Phys. Rev. D62, 054003 (2000))
• S. R. Beane, P. F. Bedaque and M. J. Savage, hep-ph/0002209.Meson Masses in High Density QCD. The low-energy effective theories for the two- and three-flavor color-superconductors arising in the high density limit of QCD are discussed. Using an effective field theory to describe quarks near the fermi surface, we compute the masses of the pseudo-Goldstone bosons that dominate the low-momentum dynamics of these systems. (Phys. Lett. B483, 131 (2000))
• F. Sannino, hep-ph/0002277.A Note on Anomaly Matching for Finite Density QCD. We note that the QCD phases at large finite density respect 't Hooft anomaly matching conditions. Specifically the spectrum of the light excitations possesses the correct quantum numbers required to obey global anomaly constraints. We argue that 't Hooft constraints can be used at finite density along with non perturbative     methods to help selecting the correct phase. (Phys. Lett. B480, 280 (2000))
• Hiranmaya Mishra and Jitendra C. Parikh, hep-ph/0003019. Chiral symmetry breaking, color superconductivity and quark matter phase diagram: a variational approach. We discuss in this note simultaneous existence of chiral symmetry breaking and color superconductivity at finite temperature and density in a Nambu-Jona-Lasinio type model. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. (Nucl. Phys. A679 (2001) 597-615)
• D. H. Rischke, nucl-th/0003063.Debye screening and Meissner effect in a three-flavor color superconductor. I compute the gluon self-energy in a color superconductor with three flavors of massless quarks. (Phys. Rev. D62, 054017 (2000))
• B. Vanderheyden and A. D. Jackson, hep-ph/0003150. Random matrix model for chiral symmetry breaking and color superconductivity in QCD at finite density. We consider a random matrix model which describes the competition between chiral symmetry breaking and the formation of quark Cooper pairs in QCD at finitedensity.(Phys. Rev. D62, 094010 (2000))
• M. Alford, hep-ph/0003185. Color superconductivity in dense quark matter. I discuss recent developments in our understanding of the color-superconducting phases of cold, dense quark matter. I describe the phase diagram as a function of density and the strange quark mass, and outline some ideas about possible observational consequences of these exotic phases. (proceedings of TMU-Yale symposium on the dynamics of gauge fields)
• W. E. Brown, J. T. Liu and H. Ren, hep-ph/0003199. Non-Fermi Liquid Behaviour, the BRST Identity in the Dense Quark-Gluon Plasma and Color Superconductivity. Screening in the plasma leads to novel behaviour, including a remarkable non-BCS scaling of T_C, the transition temperature to the color superconducting phase. Radiative corrections to one gluon exchange were previously considered and found to affect T_C. In particular, the quark self-energy in a plasma leads to non-Fermi liquid behaviour and suppresses T_C. However, at the same time, the quark-gluon vertex was shown not to modify the result at leading order. This dichotomy between the effects of the radiative corrections at first appears rather surprising, as the BRST identity connects the self-energy to the vertex corrections. Nevertheless, as we demonstrate, there is in fact no contradiction with the BRST identity, at least to leading log order. This clarifies some of the previous statements on the importance of the higher order corrections to the determination of T_C and the zero temperature gap in color superconductivity. (Phys.Rev. D62, 054013 (2000))
• V. A. Miransky, I. A. Shovkovy, L. C. R. Wijewardhana, hep-ph/0003327. Diquark composites in the color superconducting phase of two flavor dense QCD. We study the Bethe-Salpeter equations for spin zero diquark composites in the color superconducting phase of N_f=2 cold dense QCD. The explicit form of the spectrum of the diquarks, containing an infinite tower of narrow (at high density) resonances, is derived. (Nucl.Phys.Proc.Suppl. 102 (2001) 385-390)
• S. R. Beane, P. F. Bedaque and M. J. Savage, nucl-th/0004013. Renormalization Group Improved Gap Equation for Color Superconductors. The renormalization group is used to resum leading logarithmic contributions of the form alpha_s^{n+1} beta_0^n log^n (Delta/mu) to the gap equation appropriate for high density QCD. The scale dependence of the strong coupling constant alpha_s increases the gap by a factor of exp(33/16 (pi^2/4 - 1)) ~ 20 in the small coupling limit. (Nucl.Phys. A688 (2001) 931-938)
• C. Manuel, hep-ph/0005040. Dispersion Relations in Ultradegenerate Relativistic Plasmas. The propagation of excitation modes in a relativistic ultradegenerate plasma is modified by their interactions with the medium. (Phys. Rev. D62, (6009))
• S.R. Beane and P. F. Bedaque, nucl-th/0005052.How to Renormalize the Gap Equation in High Density QCD. We discuss two technical issues related to the gap equation in high-density QCD: i) how to obtain the asymptotic solution with well controlled approximations, and ii) the renormalization of four-quark operators in the high-density effective field theory. (Phys. Rev. D62, 117502 (2000))
• D. T. Son and M. A. Stephanov, hep-ph/0005225. QCD at finite isospin density. QCD at finite isospin chemical potential mu_I has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu_I where chiral perturbation theory is applicable, and at asymptotically high mu_I where perturbative QCD works. (Phys.Rev.Lett. 86 (2001) 592-595)
• Taekoon Lee, hep-ph/0005312. Chiral Vacuum Alignment in Dense QCD. We discuss an interesting possibility of nontrivial, quark-mass induced chiral vacuum alignment in color-flavor locking phase of cold, dense QCD. (Phys.Lett. B503 (2001) 307-312)
• J.T. Lenaghan, hep-ph/0005330. Influence of the U(1)_A Anomaly on the QCD Phase Transition. The SU(3)_{r} \times SU(3)_{\ell} linear sigma model is used to study the chiral symmetry restoring phase transition of QCD at nonzero temperature. The line of second order phase transitions separating the first order and smooth crossover regions is located in the plane of the strange and nonstrange quark masses. (Phys.Rev. D63 (2001) 037901).
• Chaejun Song, nucl-th/0006030. Dense Nuclear Matter: Landau Fermi-Liquid Theory and Chiral Lagrangian with Scaling. The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling("BR scaling") and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. (Phys. Rept. 347 (2001) 289-371)
• T. Schafer, hep-ph/0006034. Quark Hadron Continuity in QCD with one Flavor.  We study QCD with one flavor at finite baryon density. In the limit of very high baryon density the system is expected to be a color superconductor. In the case of     one flavor, the order parameter is in a $\bar 3$ of color and has total angular momentum one. (Phys. Rev. D62, 094007 (2000))
• S. D. Hsu, F. Sannino and M. Schwetz, hep-ph/0006059. Anomaly Matching in Gauge Theories at Finite Matter Density. We investigate the application of 't Hooft's anomaly matching conditions to gauge theories at finite matter density. We show that the matching conditions constrain the low-energy quasiparticle spectrum associated with possible realizations of global symmetries. (Mod.Phys.Lett. A16 (2001) 1871-1880)
• D. K. Hong, hep-ph/0006105. Radiative mass in QCD at high density. We show that radiatively generated Majorana mass for antiquarks is same as the Cooper-pair gap.  (Phys. Rev. D62, 091501 (2000))
• C. Manuel, hep-ph/0006106. Lifetime Effects in Color Superconductivity at Weak Coupling.  Present computations of the gap of color superconductivity in weak coupling assume that the quarks which participate in the condensation process are infinitely long-lived. However, the quasiparticles in a plasma are characterized by having a finite lifetime. (Phys. Rev. D62, 114008 (2000))
• T. Schafer, nucl-th/0007021. Kaon Condensation in High Density Quark Matter. We point out that the problem of kaon condensation in dense hadronic matter can be addressed in perturbative QCD. Indeed, perturbative calculations suggest that negative kaons are condensed in high density quark matter if the electroweak interaction is taken into account. (Phys.Rev.Lett. 85 (2000) 5531-5534)
• M. A. Nowak, M. Rho, A. Wirzba and I. Zahed, hep-ph/0007034. Pi0 -> Gamma Gamma in Dense QCD. We analyze the generalized process $\tilde\pi^0\to\tilde{\gamma}\tilde{\gamma}$ in the weak coupling limit and show that it is related to the recently suggested Wess-Zumino-Witten (WZW) term. In dense QCD, the radiative decay of the generalized pion is constrained by geometry and vanishes at large density. (Phys.Lett. B497 (2001) 85-90)
• Mannque Rho, nucl-th/0007073. Physics of dense and superdense matter. Review of dense QCD. (KIAS International Workshop on Astrophysics, Seoul, Korea, 24-27 May 2000)
• W. Mao, F. Cooper, A. Singh and A. Chodos, hep-ph/0007244.Dynamics of the chiral phase transition at finite chemical potential. Study of the chiral phase in the Gross Neveu model in the large N limit
• V. Schon and M. Thies, hep-th/0008175. 2D model field theories at finite temperature and density. Study of 2D models. Contribution to the Festschrift in honor of Boris Ioffe, edited by M. Shifman
•  R. Rapp, E. Shuryak and I. Zahed, hep-ph/0008207. A chiral crystal in cold QCD matter at intermediate densities? The analogue of Overhauser (particle-hole) pairing in electronic systems (spin-density waves with non-zero total momentum $Q$) is analyzed in finite-density QCD for 3 colors and 2 flavors, and compared to the color-superconducting BCS ground state (particle-particle pairing, $Q$=0). Employing medium-modified instanton-induced 't Hooft interactions, as applicable around $\mu_q\simeq 0.4$ GeV (or 4 times nuclear saturation     density), we find the 'chiral crystal phase' to be competitive with the color superconductor. (Phys.Rev. D63 (2001) 034008)
• Andreas Wirzba, nucl-th/0009002. Cooper-Mesons in the Color-Flavor-Locked Superconducting Phase of Dense QCD. QCD superconductors in the color-flavor-locked (CFL) phase sustain excitations (``Cooper'' mesons) that can be described as pairs of particles or holes around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy the masses, decay constants and form factors of the scalar, pseudoscalar, vector and axial-vector excitations, which explicitly are of finite size, can be calculated exactly. (invited talk for Bologna 2000)
• A. Chodos, F. Cooper, W. Mao, H. Minakata and A. Singh, hep-ph/0009019.A two-dimensional model with chiral condensates and Coopre pairs having QCD-like phase structure. Generalization of the original Gross-Neveu model from U(N) to O(N) leading to pair condensation.  )Presented at TMU-Yale Symposium on Dynamics of Gauge Fields: An External Activity of APCTP, Tokyo, Japan, 13-15 Dec 1999)
• V. A. Miransky, I. A. Shovkovy and L. C. Wijewardhana, hep-ph/0009129. Diquarks in cold dense QCD with two flavors. We derive and analyze the Bethe-Salpeter equations for spin zero diquarks in the color superconducting phase of cold dense QCD with two massless flavors. (Phys. Rev.D62, 085025 (2000))
• D. Boyanovsky and H. J. de Vega, hep-ph/0009172. Non-Fermi Liquid Aspects of Cold and Dense QED and QCD: Equilibrium and Non-Equilibrium. Infrared divergences from the exchange of dynamically screened magnetic gluons (photons) lead to the breakdown of the Fermi liquid description of the normal state of cold and dense QCD and QED. We implement a resummation of these divergences via the renormalization group to obtain the spectral density, dispersion relation, widths and wave function renormalization of single quasiparticles near the Fermi surface. (Phys.Rev. D63 (2001) 034016)
• V. A. Miransky, I. A. Shovkovy and L. C. Wijewardhana, hep-ph/0009173. Bethe-Salpeter equation for diquarks in color-flavor locked phase of cold dense QCD. The Bethe-Salpeter equations for diquarks with the quantum numbers of the Nambu-Goldstone bosons are analyzed in the color-flavor locked phase of cold dense QCD with three quark flavors. (Phys.Rev. D63 (2001) 056005)
• T. Grandou, hep-ph/0009351. Puzzling aspects of hot quantum fields. Some intriguing points of finite temperature quantum field theory are considered. (Proceedings of the 5th workshop on QCD, Villefranche-sur-Mer, 3-8 January 2000)
• E. Babaev, cond-mat/0009438. Aspects of topology of condensates and knotted solitons in two-band superconductors. Discussion of type-II superconductors with two flavors of Cooper pairs. (Animations of knotted solitons by Hietarinta and Salo are available at this http URL)
• I.A. Shovkovy, nucl-th/0010021. The Spectrum of Diquark Composites in Cold Dense QCD. The Bethe-Salpeter equations for spin zero diquark composites in the color superconducting phase of $N_f=2$ and $N_f=3$ cold dense QCD are studied. The explicit form of the spectrum of the diquarks with the quantum numbers of the (pseudo-) Nambu-Goldstone bosons is derived. (Int.J.Mod.Phys. A16S1C (2001) 1271-1273)
• T. Schaefer and E. Shuryak, nucl-th/0010049. Phases of QCD at High Baryon Density. We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. (Lect.Notes Phys. 578 (2001) 203-217)
• J.V. Steele, nucl-th/0010066. Effective field theory power counting at finite density. Power counting for finite density theory is studied.
• R.J. Furnstahl, H.-W. Hammer and Negussie Tirfessa, nucl-th/0010078. Field Redefinitions at Finite Density. The apparent dependence of nuclear matter observables on off-shell properties of the two-nucleon potential is re-examined in the context of the effective field theory (EFT) approach. (Nucl. Phys. A689 (2001) 846-868)
• Nguyen Van Hieu, hep-ph/0010154. Functional Integral Method in the Theory of Color Superconductivity. We propose to study the superconducting pairing of quarks with the formation of the diquarks as well as the quark-antiquark pairing in QCD by means of the functional integral technique. ( Invited talk given at the International Conference on Physics at Extreme Energy - Rencontres du Vietnam IV, Hanoi 19-25 July 2000)
• D.K. Hong, H.K. Lee, M.A. Nowak and M. Rho, hep-ph/0010156. Neutrino interactions in color-flavor-locked dense matter. Determination of the relevant electro-weak interactions in the CFL phase. Implications about the cooling of neutron stars.
• C. Manuel and M. Tytgat, hep-ph/0010274. Sum Rules in the CFL Phase of QCD at finite density. We study the asymmetry between the vector current and axial-vector current correlators in the colour-flavour locking (CFL) phase of QCD at finite density. Using Weinberg's sum rules, we compute the decay constant $f_\pi$ of the Goldstone modes and find agreement with previous derivations. (Phys.Lett. B501 (2001) 200-208)
• O. Philipsen, hep-lat/0011019. Static correlation lengths in QCD at high temperature and finite density. A brief review is given of the sign problem in finite density lattice QCD and various attempts to overcome it. (Nucl.Phys.Proc.Suppl. 94 (2001) 49-60)
• D. K. Hong, S.-T. Hong and Y.-J. Park, hep-ph/0011027. Bosonization of QCD at high density. We describe the color-flavor locking (CFL) color superconductor in terms of bosonic variables, where the gaped quarks are realized as solitons, so-called superqualitons. We then show that the ground state of the CFL color superconductor is a $Q$-matter, which is the lowest energy state for a given fixed baryon     number. (Phys.Lett. B499 (2001) 125-134)
• J. Hosek, hep-ph/0011033. On Superfluid Phases of Cold Deconfined QCD Matter at Moderate Baryon Density. We present an overview of the arguments which lead to the picture that at low temperatures the QCD matter not far above a critical confinement-deconfinement density exists in one of several distinct superfluid phases exhibiting the quantum behavior on macroscopic scales. (talk given at Les Rencontres de Physique de la Vallee d'Aoste, February 27 - March 4, 2000, La Thuile, Italy)
• J. Hosek, hep-ph/0011034. Anisotropic color superconductor. We argue that the QCD matter not far above a critical confinement-deconfinement baryon density and low temperatures can develop spontaneously the condensates of spin-one quark Cooper pairs. Depending upon their color these condensates characterize two distinct anisotropic color-superconducting phases.     For them we derive the generic form of the quasiquark dispersion laws and the gap equation. (talk given at ICHEP 2000 in parallel session "High Energy Heavy Ion Collisions", July 27)
•  Xiang-Qian Luo, E.B. Gregory, Shuo-Hong Guo and H. Kroger, hep-ph/0011120. QCD at Finite Density. At sufficiently high temperature and density, quantum chromodynamics (QCD) predicts phase transition from the hadronic phase to the quark-gluon plasma phase. (Proceedings of the International Workshop on Nonperturbative Methods and Lattice QCD, World Scientific (2001) 138-149)
• Kei Iida and G. Baym, hep-ph/0011229.The superfluid phases of quark matter: Ginzburg-Landau theory and color neutrality. We apply Ginzburg-Landau theory to determine BCS pairing in a strongly-coupled uniform superfluid of three-flavor massless quarks in flavor equilibrium. (Phys.Rev. D63 (2001) 074018) See also hep-ph/0108149, hep-ph/0204124
• D. Ebert, K.G. Klimenko and H. Toki, hep-ph/0011273.Chromagnetic catalysis of color superconductivity in a (2+1)-dimensional NJL model. Influence of a constant chromomagnetic field on the formation of color superconductivity is studied. (Phys.Rev. D64 (2001) 014038)
• D.T. Son and M.A. Stephanov, hep-ph/0011365. QCD at finite isospin density: from pion to quark-antiquark condensation. Study od QCD at finite isospin chemical potential. (Phys.Atom.Nucl. 64 (2001) 834-842; Yad.Fiz. 64 (2001) 899-907)
• D.H. Rischke, D.T. Son and M.A. Stephanov, hep-ph/0011379. Asymptotic deconfinement in high density QCD. We discuss QCD with two light flavors at large baryon chemical potential mu. Color superconductivity leads to partial breaking of the color SU(3) group. We     show that the infrared physics is governed by the gluodynamics of the remaining SU(2) group with an exponentially soft confinement scale Lambda_QCD' Delta*exp[-a*mu/(g*Delta)], where Delta<<mu is the superconducting gap, g is the strong coupling, and a=0.81... (Phys.Rev.Lett.87:062001,2001)
• J. Baacke, D. Cormier, H. J. de Vega and K. Heitmann, hep-ph/0011395. Dynamics of O(N) chiral supersymmetry at finite energy density. We consider an O(N) version of a massive, interacting, chiral supersymmetry model solved exactly in the large N limit. We demonstrate that the system approaches a stable attractor at high energy densities, corresponding to a non-perturbative state for which the relevant field quanta are massless. (Phys. Lett. B520 (2001) 317-321)
• M.B. Hecht, C.D. Roberts and S.M. Schmidt, nucl-th/0012023. Diquarks and Density. We describe aspects of the role that diquark correlations play in understanding baryon structure and interactions. (Lect.Notes Phys. 578 (2001) 218-234)
• D.T. Son, M.A. Stephanov, A.R. Zhitnitsky, hep-ph/0012041. Domain walls of high-dProceedings of the International Workshop on Nonperturbative Methods and Lattice QCD, World Scientific (2001) 138-149ensity QCD. We show that in very dense quark matter there must exist metastable domain walls where the axial U(1) phase of the color-superconducting condensate changes by 2pi. The decay rate of the domain walls is exponentially suppressed and we compute it semiclassically. We give an estimate of the critical chemical potential    above which our analysis is under theoretical control. (Phys.Rev.Lett. 86 (2001) 3955-3958)
• Yasuo Umino, hep-ph/0012071. Equation of state of strongly coupled Hamiltonian lattice QCD at finite density. We calculate the equation of state of strongly coupled Hamiltonian lattice QCD at finite density by constructing a solution to the equation of motion corresponding to an effective Hamiltonian using Wilson fermions.
• V.M. Lotkev, R.M. Quick and S.G. Sharapov, cond-mat/0012082. Phase fluctuations and pseudogap phenomena. Review of superconducting phase fluctuations. (Phys.Rept. 349 (2001) 1-123)
• K. Splittorff, D.T.Son and M.A. Stephanov, hep-ph/0012274. QCD-like Theories at Finite Baryon and Isospin Density. We use 2-color QCD as a model to study the effects of simultaneous presence of chemical potentials for isospin charge, $\mu_I$, and for baryon number,     $\mu_B$. (Phys.Rev. D64 (2001) 016003)
• J. Berges and C. Wetterich, hep-ph/0012311. Higgs description of two-flavor QCD vacuum. Higgs description of the QCD vacuum in the limit of two-quark flavors. (Phys.Lett. B512 (2001) 85-90)
• G.E. Brown, Mannque Rho, nucl-th/0101015. The Fate of Hadron Masses in Dense Matter: Hidden Local Symmetry and Color Flavor Locking. The notion that hadron masses scale according to the scaling of the quark condensate in hadronic matter, partly supported by a number of observations in finite nuclei, can be interpreted in terms of Harada-Yamawaki's ``vector manifestation" (VM) of chiral symmetry.
• Y. Kim, Young-Ho Song and Dong-Pil Min, hep-ph/0101189. Meson exchange effect on color superconductivity. Effects of pion and gluon exchanges on the formation of two-flavor superconductivity at moderate density, m < 1 GeV. (Phys.Rev. D64 (2001) 014026)
• J.A. Oller, hep-ph/0101204. Chiral Lagrangians at finite density. The effective SU(2) chiral Lagrangian with external sources is given in the presence of non-vanishing nucleon densities by calculating the in-medium contributions of the chiral pion-nucleon Lagrangian. (Phys.Rev. C65 (2002) 025204)
• F. Gastineau, R. Nebauer and J. Aichelin, hep-ph/0101289. Thermodynamics of the 3-flavor NJL model : chiral symmetry breaking and color superconductivity.Employing an extended three flavor version of the NJL model we discuss in detail the phase diagram of quark matter. The presence of quark as well as of diquark condensates gives raise to a rich structure of the phase diagram.
• C.Wetterich, hep-ph/0102248. Phase transition between three- and two-flavor QCD? Spontaneous breaking of color is investigated for the vacuum of QCD$_2$ with two light flavors of quarks. We classify possible colored quark-antiquark, diquark and gluon condensates that are compatible with a spectrum of integer charged states and conserved isospin and baryon number.
• D.H. Rischke, nucl-th/0103050. Gluon self-energy in a two-flavor color superconductor. The energy and momentum dependence of the gluon self-energy is investigated in a color superconductor with two flavors of massless quarks. The presence of a color-superconducting quark-quark condensate modifies the gluon self-energy for energies which are of the order of the gap parameter. (Phys.Rev. D64 (2001) 094003)
• D.T. Son, M.A. Stephanov, A.R. Zhitnitsky, hep-ph/0103099. Instanton interactions in dense-matter QCD. A Coulomb gas representation of dense-matter QCD is derived from a dual transformation of the low-energy effective Lagrangian. The point-like charges Q=+1,-1 of the gas are identified with the instantons and anti-instantons of such topological charges. An instanton repels another instanton with the same force as it attracts an anti-instanton, in contrast to the semiclassical interaction. (Phys.Lett. B510 (2001) 167-172)
• V.A. Miransky, G.W. Semenoff, I.A. Shovkovy and L.C.R. Wijewardhana, hep-ph/0103227. Color superconductivity and nondecoupling phenomena in 2+1 dimensional QCD. Study of superconductivity in 2+1 dimensional QCD. (Phys.Rev. D64 (2001) 025005)
• V.P. Gusynin and I.A. Shovkovy, hep-ph/0103269. Carlson-Goldman modes in the color superconducting phase of dense QCD. Prediction of the gapless Carlson-Godman modes in the CFL phase. (Phys.Rev. D64 (2001) 116005)
• D.T. Son, M.A. Stephanov, cond-mat/0103451. Domain walls of relative phase in two-component Bose-Einstein condensates. We consider a system of two interpenetrating Bose-Einstein condensates of atoms in two different hyperfine spin states. We show that in the presence of a small coupling drive between the two spin levels, there exist domain walls across which the relative phase of the two condensates changes by 2pi. We give the physical interpretation of such walls. (Phys.Rev. A65 (2002) 063621)
• J.B. Kogut, D. Toublan and D.K. Sinclair, hep-lat/0104010. Diquark Condensation at Nonzero Chemical Potential and Temperature. SU(2) lattice gauge theory with four flavors of quarks is studied at nonzero chemical potential $\mu$ and temperature $T$ by computer simulation and Effective Lagrangian techniques. (Phys.Lett. B514 (2001) 77-87)
• D.H. Rischke, nucl-th/0104071. Remarks on the extraction of freeze-out parameters. I review the extraction of kinetic and chemical freeze-out parameters from experimental data, with particular emphasis on the underlying assumptions and the validity of the conclusions. (Nucl.Phys. A698 (2002) 153-163)
• P. F. Bedaque and T. Schaefer, hep-ph/0105150. High Density Quark Matter under Stress. We study the effect of SU(3) flavor breaking on high density quark matter. We discuss, in particular, the effect a non-zero electron chemical potential and a finite strange quark mass. We argue that these perturbations trigger pion or kaon condensation. (Nucl.Phys. A697 (2002) 802-822)
• D.F. Litim and C. Manuel, hep-ph/0105165. Photon Self-Energy in a Color Superconductor. In a color superconductor the diquark condensates break spontaneously both the color and ordinary electromagnetism, leaving a remanining rotated U(1) symmetry unbroken. The gauge interactions associated to this rotated symmetry may be considered as the in-medium electromagnetism. We compute the in-medium photon self-energy in the presence of diquark condensates at high baryonic density and weak coupling. (Phys.Rev. D64 (2001) 094013)
• O. Kiriyama, S. Yasui, H. Toki, hep-ph/0105170. Color superconductivity at finite density and temperature with flavor asymmetry. Color superconductivity of QCD at finite density, temperature and flavor asymmetry is studied within an approximation which the interaction is modeled upon four--fermion interactions. (Int.J.Mod.Phys. E10 (2001) 501-510)
• A. Rebhan, hep-ph/0105183. Thermal gauge firld theories. Review of real and imaginary time formalisms of thermal field theory. (Lectures delivered at the 40th Schladming Winter School on ``Dense Matter'', Lect. Notes Phys. 583 (2002) 161-208)
• N. Van Hieu, hep-ph/0105286. Functional integral method in quantum theory of composite particles and quasiparticles. Functional integral methods for bound states. (Lectures at the 7-th International School in Theoretical Physics, Hanoi 23 December 2000-05 January 2001)
• N. Van Hieu, hep-ph/0105343. Functional approach in the theory of color superconductivity. Study of superconductivity with functional methods. (Phys.Part.Nucl. 33 (2002) 37-51; Fiz.Elem.Chast.Atom.Yadra 33 (2002) 72-100)
• Z. Fodor and S.D. Katz, hep-lat/0106002. Lattice determination of the critical point of QCD at finite T and mu. Based on universal arguments it is believed that there is a critical point (E) in QCD on the temperature (T) versus chemical potential (\mu) plane, which is of extreme mportance for heavy-ion experiments. Using finite size scaling and a recently proposed lattice method to study QCD at finite \mu we determine the location of E in QCD with n_f=2+1 dynamical staggered quarks with semi-realistic masses on $L_t=4$ lattices. Our result is T_E=160 \pm 3.5 MeV and \mu_E=725 \pm 35 MeV. For the critical temperature at \mu=0 we obtained T_c=172 \pm 3 MeV. (JHEP 0203 (2002) 014)
• B.O. Kerbikov, hep-ph/0106324. Anderson theorem for color superconductor. Derivation of the Ginsburg-Landau functional for system with diverse condensates and proof of the Anderson theorem
• F. Karsch, E. Laermann, Ch. Schmidt, hep-lat/0107020. The Chiral Critical Point in 3-Flavour QCD. We determine the second order endpoint of the line of first order phase transitions, which occur in the light quark mass regime of 3-flavour QCD at finite temperature, and analyze universal properties of this chiral critical point. (Phys.Lett. B520 (2001) 41-49)
• J.T. Lenaghan, F. Sannino and K. Splittorff, hep-ph/0107099. The Superfluid and Conformal Phase Transitions of Two-Color QCD. The phase structure of two-color QCD is examined as a function of the chemical potential and the number of light quark flavors. We consider effective Lagrangians for two-color QCD containing the Goldstone excitations, spin-one particles and negative intrinsic parity terms. We discuss the possibility of a conformal phase transition and the enhancement of the global symmetries as the number of flavors is increased. (Phys.Rev. D65 (2002) 054002)
• D. Kharzeev, E. Levin, nucl-th/0108006. Manifestations of high density QCD in the first RHIC data. We derive a simple analytical scaling function which embodies the predictions of high density QCD on the energy, centrality, rapidity, and atomic number dependences of hadron multiplicities in nuclear collisions. Both centrality and rapidity dependences of hadron multiplicity in $Au-Au$ collisions as measured at     RHIC at $\sqrt{s}= 130 {GeV}$ are well described in this approach. (Phys.Lett. B523 (2001) 79-87)
• S. Mallik, hep-th/0108139. Scattering amplitude and shift in self-energy in medium. Two simple proofs are presented for the first order virial expansion of the self-energy of a particle moving through a medium, characterised by temperature and/or chemical potential(s). One is based on the virial expansion of the self-energy operator itself, while the other is on the analysis of its Feynman diagrams in configuration space. (Eur.Phys.J. C24 (2002) 143-147)
• Kei Iida and G. Baym, hep-ph/0108149. Superfluid phases of quark matter, II: Phenomenology and sum rules. We derive sum rules for a uniform, isotropic superfluid quark-gluon plasma with massless quarks, first laying out the phenomenological equations obeyed by a     color superconductor in terms of macroscopic observables such as the superfluid mass and baryon densities, and the electric and magnetic gluon masses, and then expressing these quantities in terms of equilibrium correlation functions. (Phys.Rev. D65 (2002) 014022)
• Masayasu Harada, Satoshi Takagi, hep-ph/0108173. Phase Transition in Dense QCD with the Schwinger-Dyson Equation. We investigate the phase structure of dense QCD using the Schwinger-Dyson equation (SDE) with the improved ladder approximation in the Landau gauge. We  use the gluon propagator with the electric mode corrected by Debye screening and the magnetic mode corrected by Landau damping. (Prog.Theor.Phys. 107 (2002) 561-596)
• V. P. Gusynin, I. A. Shovkovy, hep-ph/0108175. Collective modes of color-flavor locked phase of dense QCD at finite temperature. A detailed analysis of collective modes that couple to either vector or axial color currents in color-flavor locked phase of color superconducting dense quark matter at finite temperature is presented. Among the realm of collective modes, including the plasmons and the Nambu-Goldstone bosons, we also reveal the gapless Carlson-Goldman modes, resembling the scalar Nambu-Golstone bosons. (Nucl.Phys. A700 (2002) 577-617)
• V. A. Miransky, I. A. Shovkovy, hep-ph/0108178. Spontaneous Symmetry Breaking with Abnormal Number of Nambu-Goldstone Bosons and Kaon Condensate. We describe a class of relativistic models incorporating finite density of matter in which spontaneous breakdown of continuous symmetries leads to a lesser number of Nambu-Goldstone bosons than that required by the Goldstone theorem. (Phys.Rev.Lett. 88 (2002) 111601)
• T. Schaefer, D.T. Son, M.A. Stephanov, D. Toublan, J.J.M. Verbaarschot, hep-ph/0108210. Kaon Condensation and Goldstone's Theorem.  We consider QCD at a nonzero chemical potential for strangeness. At a critical value of the chemical potential equal to the kaon mass, kaon condensation occurs through a continuous phase transition. We show that, when the isospin symmetry is exact in the Lagrangian, a Goldstone boson with a dispersion relation $E \sim p^2$ appears in the kaon condensed phase. At the same time, the number of the Goldstone bosons is less than the number of broken generators. (Phys.Lett. B522 (2001) 67-75)
• Hiroaki Abuki, Tetsuo Hatsuda and Kazunori Itakura, hep-ph/0109013. Structural Change of Cooper Pairs and Momentum-dependent Gap in Color Superconductivity. The two-flavor color superconductivity is studied over a wide range of baryon density with a single model. We pay a special attention to the spatial-momentum dependence of the gap and to the spatial-structure of Cooper pairs. (Phys.Rev. D65 (2002) 074014)
• T. Schaefer, nucl-th/0109029. Strange Goings on in Quark Matter. We review recent work on how the superfluid state of three flavor quark matter is affected by non-zero quark masses and chemical potentials. (Proceedings of 6th Workshop on Non-Perturbative QCD, Paris, France, 5-9 Jun 2001)
• K. Langfeld, hep-lat/0109033. Confinement versus color superconductivity: a lattice investigation. High density YM-theory is addressed by means of an effective theory where a Higgs type field corresponds to the diquark order parameter. The effective Higgs theory mimics the Cooper instability at the Fermi surface. (contribution to 'Statistical QCD', Bielefeld, August 26-30, 2001)
• S. Hands, hep-lat/0109034. Lattice Matter. I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color QCD; and (c) Fermi surface effects in the NJL model. Some remarks are made concerning the relation of superconductivity with the sign problem. (Nucl.Phys.Proc.Suppl. 106 (2002) 142-150)
• T. Schaefer, hep-ph/0109052.  Mass Terms in Effective Theories of High Density Quark Matter. We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for     Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Sch\"afer. We show that to leading order in the coupling constant $g$ there is no anti-particle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge. (Phys.Rev. D65 (2002) 074006)
• M. Buballa, M. Oertel, hep-ph/0109095. Color-Flavor Unlocking and Phase Diagram with Self-Consistently Determined Strange Quark Masses. The phase diagram of strongly interacting matter at non-zero temperature and baryon chemical potential is calculated within a 3-flavor NJL-type quark model with realistic quark masses. The model exhibits spontaneous chiral symmetry breaking as well as diquark condensation in the two-flavor color-superconducting phase and in the color-flavor locked phase. We investigate the color-flavor unlocking phase transition, taking into account self-consistently calculated effective quark masses. We find that it is mainly triggered by a first order phase transition with respect to the strange quark mass. It takes place at much higher values of the chemical potential than the transition to the hadronic phase such that we find a relatively large region in the phase diagram where the two-flavor color-superconductor seems to be the most favored state. (Nucl.Phys. A703 (2002) 770-784)
•  C.M. Varma, cond-mat/0109409. Higgs Boson in Superconductors. Superfluid helium, describable by a two-component order parameter, exhibits only the Bogolubov mode with energy $\to 0$ at long wavelengths, while a Lorentz-invariant theory with a two-component order parameter exhibits a finite energy mode at long wavelengths (the Higgs Boson), besides the above mass-less mode.
• Qun Wang and D.H. Rischke, nucl-th/0110016. How the quark self-energy affects the color-superconducting gap. We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the     color-superconducting gap parameter to subleading order in the QCD coupling constant $g$ at zero temperature. At this order in $g$, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter $\f_0$ by a factor $b_0'=\exp \big[ -(\p ^2+4)/8 \big]\simeq 0.177$. On the other hand, the BCS relation $T_c\simeq 0.57\f_0$ between $\f_0$ and the transition temperature $T_c$ is shown to remain valid after taking into account corrections from the quark self-energy. The resulting value for $T_c$ confirms a result obtained previously with a different method. Phys.Rev. D65 (2002) 054005)
• Mei Huang, Pengfei Zhaung, Weiqin Chao, hep-ph/0110046. Massive Quark Propagator in the Color-superconducting Phase. A more general expression for the quark propagator including both chiral and diquark condensates has been derived by using energy projectors. This makes it possible to study the phase transition from hadron phase to color superconductivity phase in the moderate baryon density region by using Feynman diagrammatic method or Green-function method.
• P.F. Bedaque, nucl-th/0110049. Charged kaon condensation in high density quark matter. We show that at asymptotically high densities the ``color-flavor-locked + neutral kaon condensate'' phase of QCD develops a {\it charged} kaon condensate through the Coleman-Weinberg mechanism. At densities achievable in neutron stars a charged kaon condensate forms only for some (natural) values of the low energy constants describing the low-lying excitations of the ground state. (Phys.Lett. B524 (2002) 137-143)
• E.V.Shuryak, hep-ph/0110130. The QCD Phase Diagram, Equation of State, and Heavy Ion Collisions. After some historic remarks and a brief summary of recent theoretical news about the QCD phases, we turn to the issue of freeze-out in heavy ion collisions. (Invited talk at "Statistical QCD", Bielefeld, Sept.2001)
• B.O. Kerbikov, hep-ph/0110197. Color Superconducting State of Quarks. An introductory review of physics of color superconducting state of matter is presented. Comparison with superconductivity in electron systems reveals difficulties involved in formulating color superconductivity theory at moderately ultra-nuclear density.
• Youngman Kim, Dong-Pil Min and Mannque Rho, hep-ph/0110223. Kaon Condensation and Enforced Charge Neutrality of the Color-Flavor Locked Phase. We investigate the influence of charged kaon condensation in hadronic sector on the formation of the electron-free charge neutral quark matter of equipartition of three light flavors, i.e., a phenomenon called ``enforced electrical neutrality" of the color-flavor locked (CFL) phase.
• P. Amore, M. C. Birse, J.A. McGovern and N.R. Walet, hep-ph/0110267. Colour superconductivity in finite systems. In this paper we study the effect of finite size on the two-flavour colour superconducting state. As well as restricting the quarks to a box, we project onto states of good baryon number and onto colour singlets, these being necessary restrictions on any observable ``quark nuggets''. We find that whereas finite size alone has a significant effect for very small boxes, with the superconducting state often being destroyed, the effect of projection is to restore it again. The infinite-volume limit is a good approximation even for quite small systems. (Phys.Rev. D65 (2002) 074005)
• A. Rebhan, hep-ph/0111341. Hard thermal loops and QCD thermodynamics. These lectures give an introduction to thermal perturbation theory, hard thermal loops, and their use in a nonperturbative, approximately self-consistent resummation of the thermodynamical potentials of quantum chromodynamics. (Lectures given at the NATO Advanced Study Institute ``QCD perspectives on hot and dense matter'', August 6-18, 2001, in Carg\`ese, Corsica, France)
• I.A. Shovkovy, hep-ph/0110352. Collective modes in color superconducting matter. The properties of plasmons, Nambu-Goldstone bosons and gapless Carlson-Goldman collective modes in color-flavor locked phase of color superconducting dense quark matter at finite temperature are reviewed. A possibility of a kaon condensation with an abnormal number of the NG bosons is also discussed. (Int.J.Mod.Phys. A17 (2002) 904-913)
• R.D. Pisarski, D.H. Rischke, nucl-th/0111070. Gauge invariance of the color-superconducting gap on the mass shell. The gap parameter for color superconductivity is expected to be a gauge invariant quantity, at least on the appropriate mass shell. Computing the gap to subleading order in the QCD coupling constant, g, we show that the prefactor of the exponential in 1/g is gauge dependent off the mass shell, and independent of gauge on the mass shell. (Proceedings of the Conference on Statistical QCD, Bielefeld, August 26 - 30, 2001)
• D.T. Son, M.A. Stephanov, hep-ph/0111100. Pion Propagation near the QCD Chiral Phase Transition. We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition. (Phys.Rev.Lett. 88 (2002) 202302)
• Mei Huang, Pengfei Zhaung, Weiqin Chao, hep-ph/0112124. Massive quark propagator and competition between chiral and diquark condensate. The Green-function approach has been extended to the moderate baryon density region in the framework of an extended Nambu--Jona-Lasinio model, and the thermodynamic potential with both chiral and diquark condensates has been evaluated by using the massive quark propagator. (Phys.Rev. D65 (2002) 076012)
• K.B.W. Buckley, hep-ph/0112144. Classical stability of U(1)_A domain walls in dense matter QCD. It was recently shown that there exists metastable U(1)_A domain wall configurations in high-density QCD (\mu >> 1 GeV). In the following we will assess the stability of such non-trivial field configurations at intermediate densities (\mu < 1 GeV). The existence of such configurations at intermediate densities could have interesting consequences for the physics of neutron stars with high core density.  (Phys.Rev. D65 (2002) 125011)
• Tadafumi Ohsaku, cond-mat/0112456. BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation. We investigate the BCS and generalized BCS theories in the relativistic quantum field theory. We select the gauge freedom as U(1), and introduce a BCS-type effective attractive interaction. (Phys.Rev. B65 (2002) 024512). See also cond-mat/0201292
• T. Schafer, nucl-th/0201031. Superdense Matter. We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density. (Talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001)
• T. Schafer, hep-ph/0201189. Instanton Effects in QCD at High Baryon Density. We study instanton effects in QCD at very high baryon density. In this regime instantons are suppressed by a large power of $(\Lambda_{QCD}/\mu)$, where $\Lambda_{QCD}$ is the QCD scale parameter and $\mu$ is the baryon chemical potential.
• Tadafumi Ohsaku, cond-mat/0201292. BCS and Generalized BCS Superconductivity in Relativistic Quantum Field Theory. II. Numerical Calculations. We solve numerically various types of the gap equations developed in the relativistic BCS and generalized BCS framework, presented in part I of this paper. See also cond-mat/0112456
• M. Sadzikowski and M. Tachibana, hep-ph/0201223. Andreev reflection at QGP/CFL interface. In this letter we address the question of the phenomena of Andreev reflection between the cold quark-gluon plasma phase and CFL color superconductor. We show that there are two different types of reflections connected to the structure of the CFL phase. We also calculate the probability current at the interface and we show that it vanishes for energy of scattering quarks below the superconducting gap.
• M. Oertel and M. Buballa, hep-ph/0202098. Color-Flavor (Un)locking. The structure of the phase diagram of strongly interacting matter at moderate densities is calculated within a 3-flavor NJL-type quark model with realistic quark masses. We focus on the influence of the selfconsistently determined effective strange quark mass on the color-flavor unlocking phase transition. (proceedings of the workshop "Ultrarelativistic heavy ion collisions", Hirschegg 2002)
• C.P. Hofmann, cond-mat/0202153. Ferromagnets and antiferromagnets in the effective Lagrangian perspective. Nonrelativistic systems exhibiting collective magnetic behavior are analyzed within the framework of effective Lagrangians. The method, which formulates the     dynamics of the system in terms of Goldstone bosons, allows to investigate the consequences of spontaneous symmetry breaking from a unified point of view. (Contributed Talk at 8th Mexican Workshop on Particles and Fields, Zacatecas, Mexico, 14-20 Nov 2001)
• R. A. Schneider, T. Renk and W. Weise, hep-ph/0202180. Quasiparticles in QCD thermodynamics and applications. We propose a novel quasiparticle interpretation of the equation of state of deconfined QCD at finite temperature. Using appropriate thermal masses, we introduce 
a phenomenological parametrization of the onset of confinement in the vicinity of the phase transition. (Talk given at the International Workshop XXX on Gross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria)
• Deog Ki Hong, Stephen D.H. Hsu, hep-ph/0202236. Positivity of High Density Effective Theory. We show that the effective field theory of low energy modes in dense QCD has positive Euclidean path integral measure. The complexity of the measure of QCD at finite chemical potential can be ascribed to modes which are irrelevant to the dynamics at sufficiently high density. Rigorous inequalities follow at asymptotic density. Lattice simulation of dense QCD should be possible using the quark determinant calculated in the effective theory.
• K.B.W. Buckley and A,R. Zhitnitsky, hep-ph/0204064. Superconducting K strings in high density QCD. Recently it has been argued that the ground state of high density QCD is likely be a combination of the CFL-phase along with condensation of the K^0 field. This state spontaneously breaks a global U(1)_Y symmetry, therefore one would expect the formation of U(1)_Y global strings. (JHEP 0208 (2002) 013)
• M. Buballa, J. Hosek, M. Oertel, hep-ph/0204275. Anisotropic admixture in color-superconducting quark matter. The analysis of color-superconducting two-flavor deconfined quark matter at moderate densities is extended to include a particular spin-1 Cooper pairing of those quarks which do not participate in the standard spin-0 diquark condensate: (i) Due to the peculiar form of the gap equation, exhibiting spontaneous breakdown of rotational symmetry, the corresponding gap parameter Delta' is extremely sensitive to details of the effective interaction and to the chemical potential. (ii) The critical temperature of the anisotropic component is approximately given by the relation T_c'\simeq Delta'(T=0)/3. (iii) In the chiral limit the gas of anisotropic Bogolyubov-Valatin quasiquarks becomes effectively gapless and two-dimensional. Consequently, its specific heat depends quadratically on temperature. (iv) All collective Nambu-Goldstone excitations of the anisotropic phase have a linear dispersion law and the whole system remains a superfluid.
  
•  Kei Iida and G. Baym, hep-ph/0204124. Superfluid phases of quark matter. III. Supercurrents and vortices. We study, within Ginzburg-Landau theory, the responses of three-flavor superfluid quark-gluon plasmas to external magnetic fields and rotation, in both the color-flavor locked and isoscalar color-antitriplet diquark phases near the critical temperature. (Phys.Rev. D66 (2002) 014015)
• D.T. Son, hep-ph/0204199. Low-Energy Quantum Effective Action for Relativistic Superfluids. We consider relativistic superfluids where the U(1) baryon symmetry is spontaneously broken. Using the formalism of the quantum effective action, we show that the low-energy dynamics of the superfluid Goldstone boson is completely determined by the equation of state.
• D.T. Son, M.A. Stephanov, hep-ph/0204226. Real-time pion propagation in finite-temperature QCD. We argue that in QCD near the chiral limit, at all temperatures below the chiral phase transition, the dispersion relation of soft pions can be expressed entirely in terms of three temperature-dependent quantities: the pion screening mass, a pion decay constant, and the axial isospin susceptibility. The definitions of these quantities are given in terms of equal-time (static) correlation functions. Thus, all three quantities can be determined directly by lattice methods. The precise meaning of the Gell-Mann--Oakes--Renner relation at finite temperature is given.
  
• M. Buballa, M. Oertel, hep-ph/0205027. Color superconductivity in two- and three-flavor systems at moderate densities. Basic features of color superconductivity are reviewed, focusing on the regime of ``moderate densities'', which is not accessible by perturbation theory. We discuss the standard picture of two- and three flavor color superconductors and study the color-flavor unlocking phase transition within an NJL-type model. (Proceedings of the NATO Advanced Research Workshop on Confinement, Topology, and other Non-Perturbative Aspects of QCD, Stara Lesna, Slovakia, Jan 21-27, 2002)
• D.H. Rischke and I.A. Shovkovy, nucl-th/0205080. Longitudinal gluons and Nambu-Goldstone bosons in a two-flavor color superconductor. In a two-flavor color superconductor, the SU(3)_c gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of 't Hooft gauge.
• V.A. Miransky, I.A. Shovkovy, hep-ph/0205348. Magnetic catalysis and anisotropic confinement in QCD. The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. (Phys. Rev. D 66 (2002) 045006)
• T.D. Fugleberg, hep-ph/0206033. General Quasiparticle Propagator and Mass Dependence in Degenerate Color Superconductivity. The general quasiparticle propagator in dense quark matter is derived for equal mass quarks. Specialized to an NJL model, this propagator includes one new condensate, $\Delta_3$, in addition to the usual CFL condensate, $\Delta_1$.
• Mei Huang, Pengfei Zhuang and Weiqin Chao, hep-ph/0207008. Charge Neutrality Effects on 2-flavor Color Superconductivity. The effect of electric and color neutrality on 2-flavor color superconductivity has been investigated. It has been found that the effect of the charge eutrality on a 2-flavor quark system is very different from that on a 3-flavor system.
• E. Gubankov, hep-ph/0208015. Color superconductivity from magnetic interaction induced by flow equations. Using flow equations, we derive an effective quark-quark interaction and obtain the coupled set of gap equations for the condensates of the CFL phase of massless N_f=3 dense QCD. We find two different sources of the infrared cutoff in magnetic interaction. When the penetration depth of the magnetic field inside the superconductor is less than the coherence length of quark-quark bound state, our results for the gap agree with those of Son. In the other case, we obtain parametric enhancement of the gap on the coupling constant.
• M. Sadzikowski and Motoi Tachibana, hep-ph/0208037. Andreev reflection in superconducting QCD. In this paper we discuss the phenomenon of the Andreev reflection of quarks at the interface between the 2SC and the Color-Flavor-Locked (CFL) superconductors appeared in QCD at asymptotically high densities. We also give the general introduction to the Andreev reflection in the condensed matter     systems as well as the review of this subject in high density QCD.
• F. Cooper and V.M. Savage, hep-ph/0208057. Dynamics of the chiral phase transition in the 2+1 dimensional Gross-Neveu model. The phase diagram of the Gross-Neveu (G-N) model in 2+1 dimensions as a function of chemical potential and temperature has a simple curve separating the broken symmetry and unbroken symmetry phases, with chiral symmetry being restored both at high temperature and high density.
• E. Gubankova, hep-ph/0209033. Diquark interaction and gaps for color superconductivity. Using flow equations, we derive an effective quark-quark interaction and obtain the coupled set of gap equations for the condensates of the CFL phase of massless $N_f=3$ dense QCD. The formalism developed here enables one to consider more general case of nonzero $s$-quark mass.  
• Kazunori Itakura, hep-ph/0209081. Structure change of Cooper pairs in color superconductivity. Crossover from BCS to BEC? We discuss a possibility of transition from color superconductivity of the standard BCS type at high density, to Bose-Einstein Condensation (BEC) of Cooper pairs at lower density. Examining two-flavor QCD over a wide range of baryon density, we found the size of a Cooper pair becomes small enough to be comparable to the averaged quark-quark distance at lower density. We also consider the same problem in two-color QCD. 
• Tadafumi Ohsaku, cond-mat/0209352 (+ Figs). Superconductivity in (2+1)-dimensional Relativistic Quantum Field Theory. We investigate the superconductivity in (2+1)-dimensional relativistic quantum field theory. We employ the massless Gross-Neveu model as a model Lagrangian. By using this model, we study the superconductivity and superconducting instability. Our investigation is strongly related to the superconductivity in (2+1)-dimensional two-band systems. 
• A. Schmitt, Qun Wang and D.K. Rischke, nucl-th/0209050. Study of color SC for N_f=1,2,3. The leading order for the gap equation is the same in all cases. Various cases are studied in a unified way and T_c is evaluated.
• M. D'Elia, M.P. Lombardo, hep-lat/0209146. Finite density QCD via imaginary chemical potential. We study QCD at nonzero temperature and baryon density in the framework of the analytic continuation from imaginary chemical potential. We carry out simulations of QCD with four flavor of staggered fermions, and reconstruct the phase diagram in the temperature-imaginary \mu plane. We consider ans\"atze for the analytic continuation of the critical line and other observables motivated both by theoretical considerations and mean field calculations in four fermion models and random matrix theory. We determine the critical line, and the analytic continuation of the chiral condensate, up to \mu_B approx. 500 MeV. The results are in qualitative agreement with the predictions of model field theories, and consistent with a first order chiral transition. The correlation between the chiral transition and the deconfinement transition observed at \mu=0 persists at nonzero density. 
• I. Zakout, H.R. Jaqaman, W. Greiner, hep-ph/0209342. Numerical solution of the color superconductivity gap in a weak coupling constant. We present the numerical solution of the full gap equation in a weak coupling constant $g$. It is found that the standard approximations to derive the gap equation to the leading order of coupling constant are essential for a secure numerical evaluation of the logarithmic singularity with a small coupling constant. The approximate integral gap equation with a very small $g$ should be inverted to a soft integral equation to smooth the logarithmic singularity near the Fermi surface. The full gap equation is solved for a rather large coupling constant $g\ge 2.0$. The approximate and soft integral gap equations are solved for small $g$ values. When their solutions are extrapolated to larger $g$ values, they coincide the full gap equation solution near the Fermi surface. Furthermore, the analytical solution matches the numerical one up to the order one O(1). Our results confirm the previous estimates that the gap energy is of the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV. They also support the validity of leading approximations applied to the full gap equation to derive the soft integral gap equation and its analytical solution near the Fermi surface. 
• Andrew W. Steiner, Sanjay Reddy, Madappa Prakash, hep-ph/0205201. Color-Neutral Superconducting Quark Matter. We investigate the consequences of enforcing local color neutrality on the color superconducting phases of quark matter by utilizing the Nambu-Jona-Lasinio model supplemented by diquark and the t'Hooft six-fermion interactions. In neutrino free matter at zero temperature, color neutrality guarantees that the number densities of u, d, and s quarks in the Color-Flavor-Locked (CFL) phase will be equal even with physical current quark masses. Electric charge neutrality follows as a consequence and without the presence of electrons. In contrast, electric charge neutrality in the less symmetric 2-flavor superconducting (2SC) phase with ud pairing requires more electrons than the normal quark phase. The free energy density cost of enforcing color and electric charge neutrality in the CFL phase is lower than that in the 2SC phase, which favors the formation of the CFL phase. With increasing temperature and neutrino content, an unlocking transition occurs from the CFL phase to the 2SC phase with the order of the transition depending on the temperature, the quark and lepton number chemical potentials. The astrophysical implications of this rich structure in the phase diagram, including estimates of the effects from Goldstone bosons in the CFL phase, are discussed.
• Prashanth Jaikumar, Ismail Zahed, hep-ph/0209249. Scalar-isoscalar excitation in dense quark matter. We study the spectrum of scalar-isoscalar excitations in the color-flavor locked phase of dense quark matter. The sigma meson in this phase appears as a four-quark state (of diquark and anti-diquark) with a well-defined mass and extremely small width, as a consequence of it's small coupling to two pions. The quark particle/hole degrees of freedom also contribute significantly to the correlator just above the threshold 2\Delta where \Delta is the superconducting gap.
  
• Bang-Rong Zhou, hep-th/0210023. Critical analyses of order parameter and phase transitions at high density in Gross-Neveu and Nambu-Jona-Lasinio model. Based on gap equations and effective potentials derived from them we have analyzed behaviors of dynamical fermion mass near critical chemical potentials in four-fermion interaction models and proven that the symmetry restoring phase transitions at high density are second order in time-space dimension D=2 Gross-Neveu (GN) model when temperature is high and in D=3 GN model and D=4 Nambu-Jona-Lasinio (NJL) model when temperature is finite. However, when temperature goes to zero the phase transition will be first order in D=2 and D=3 GN model and still second order in D=4 NJL model. The researches not only reproduce the known most essential results in D=2 and D=3 GN model and further strengthen the conclusion in D=4 NJL model, but also indicate that the gap equations alone are fully effective for critical analyses of second order even some first order phase transitions, and after combined with the derived effective potentials, are also effective for critical analyses of general first order phase transitions. 
• M. Sadzikowski, hep-ph/0210065. Non-uniform chiral boundary between normal and superconducting phases. We show that the superconducting 2SC phase at high density and normal chiraly broken quark phase at low density is separated by the mixed non-uniform phase along the baryon density line. 
• F. Neumann, M. Buballa, M. Oertel, hep-ph/0210078. Mixed phases of color superconducting quark matter. We examine electrically and color neutral quark matter in beta-equilibrium focusing on the possibility of mixed phases between different color superconducting phases. To that end we apply the Gibbs criterion to ensure phase equilibrium and discuss the external conditions under which these mixed phases can occur. Neglecting surface and Coulomb effects we find a rich structure of different mixed phases with up to four components, including 2SC and CFL matter as well as more ``exotic'' components, like a phase with us- and ds-pairing but without ud-pairing. Preliminary estimates indicate, however, that the mixed phases become unstable if surface and Coulomb effects are included.
• M.G. Alford, J.A. Bowers, J.M. Cheyne, G.A. Cowan, hep-ph/0210106. Single color and single flavor color superconductivity. We survey the non-locked color-flavor-spin channels for quark-quark (color superconducting) condensates in QCD, using an NJL model. We also study isotropic quark-antiquark (mesonic) condensates. We make mean-field estimates of the strength and sign of the self-interaction of each condensate, using four-fermion interaction vertices based on known QCD interactions. For the attractive quark pairing channels, we solve the mean-field gap equations to obtain the size of the gap as a function of quark density. We also calculate the dispersion relations for the quasiquarks, in order to see how fully gapped the spectrum of fermionic excitations will be. We use our results to specify the likely pairing patterns in neutral quark matter, and comment on possible phenomenological consequences. 
• S. Takagi, hep-ph/0210227. Phase Structure of Hot and/or Dense QCD with the Schwinger-Dyson Equation. We investigate the phase structure of hot and/or dense QCD using the Schwinger-Dyson equation (SDE) with the improved ladder approximation in the Landau gauge. We show that the phase transition from the two-flavor color superconducting (2SC) phase to the quark-gluon plasma (QGP) phase is of second order, and that the scaling properties of the Majorana mass gap and the diquark condensate are consistent with the mean field scaling. We examine the effect of antiquark contribution, and find that setting the antiquark Majorana mass equal to the quark one is a good approximation in the medium density region. We also study the effect of the Debye screening mass of gluon, and find that neglection of it moves the critical lines to the higher temperature and higher chemical potential region. 
• C. Manuel, S. Mrowczynski, hep-ph/0206209. QCD effective actions from the solutions of the transport equations. We solve the collisionless transport equations of a quark-gluon plasma interacting through mean chromodynamic fields. The system is assumed to be translation invariant in one or more space-time directions. We present exact solutions that hold if the vector gauge fields in the direction of the translation invariance commute with their covariant derivatives. We also solve the equations perturbatively when the commutation condition is relaxed. Further, we derive the color current and the associated effective action. For the static quasi-equilibrium system, our results reproduce the full one-loop effective action of QCD in the presence of constant background fields, where the above mentioned commutation condition is satisfied. 
• I.A. Shovkovy, P.J. Ellis, hep-ph/0211049. Optically opaque color-flavor locked phase inside compact stars. The contribution of thermally excited electron-positron pairs to the bulk properties of the color-flavor locked quark phase inside compact stars is examined. The presence of these pairs causes the photon mean free path to be much smaller than a typical core radius ($R_{0} \simeq 1$ km) for all temperatures above 25 keV so that the photon contribution to the thermal conductivity is much smaller than that of the NG bosons. We also find that the electron and positron contributions to the total thermal energy of the quark core is considerably smaller than the contribution of the NG bosons and photons. These electron-positron pairs dominate the electrical conductivity since their masses are considerabley smaller than those of the lightest charged pseudo-NG bosons. 
• G. Lugones, J. E. Horvath, hep-ph/0211070 +Figs.. Color-flavor locked strange matter. We analyze how the CFL states in dense matter work in the direction of enhancing the parameter space for absolutely stable phases (strange matter). We find that the "CFL strange matter" phase can be the true ground state of hadronic matter for a much wider range of the parameters of the model (the gap of the QCD Cooper pairs $\Delta$, the strange quark mass $m_s$ and the Bag Constant $B$) than the state without any pairing, and derive a full equation of state and an accurate analytic approximation to the lowest order in $\Delta$ and $m_{s}$ which may be directly used for applications. The effects of pairing on the equation of state are found to be small (as previously expected) but not negligible and may be relevant for astrophysics. (Phys. Rev.  D 66, 074017 (2002))
• K. Splittorff, J.T. Lenaghan, J. Wirstam, hep-ph/0211086. Fluctuation Induced Critical Behavior at Non-Zero Temperature and Chemical Potential. The presence of a chemical potential explicitly breaks Lorentz invariance and may additionally break other internal symmetries. This introduces new subtleties in the determination of the critical properties of field theories at nonzero temperature. In this article, we discuss the occurrence of phase transitions in relativistic systems as a function of both chemical potential and temperature. We find that the $\epsilon$-expansion at nonzero chemical potential is not affected by the explicit breaking of Lorentz invariance but is sensitive to the breaking of additional symmetries by the chemical potential. We derive effective three dimensional theories at criticality and study the effect of the chemical potential on the fixed point structure of the $\beta$-functions within several different contexts: first for a scalar field theory with a global U(1) symmetry, then for the chiral phase transition in QCD with two colors and two flavors, and finally, we consider QCD with three colors at nonzero baryon and isospin chemical potential. 
• H. Müther, A. Sedrakian, hep-ph/0212317. Breaking rotational symmetry in two-flavor color superconductors. The color superconductivity under flavor asymmetric conditions relevant to the compact star phenomenology is studied within the Nambu-Jona-Lasinio model. We focus on the effect of the deformation of the Fermi surfaces on the pairing properties and the energy budget of the superconducting state. We find that at finite flavor asymmetries the color superconducting BCS state is unstable towards spontaneous quadrupole deformation of the Fermi surfaces of the $d$ and $u$ quarks into ellipsoidal form. The ground state of the phase with deformed Fermi surfaces corresponds to a superposition of prolate and oblate deformed Fermi ellipsoids of $d$ and $u$ quarks. 
• F. Sannino,  hep-ph/0301035. Anomaly Matching and Low Energy Theories at High Matter Density. I provide new arguments supporting the validity of the t'Hooft anomaly conditions at non zero quark chemical potential. These constraints strengthen the quark-hadron continuity scenario. Finally I review the 2SC effective Lagrangian for color superconductivity.  
• D. Blaschke, M. K. Volkov, V.L.Yudichev, hep-ph/0301065. Coexistence of color superconductivity and chiral symmetry breaking within the NJL model. The phase diagram for quark matter is investigated within a simple Nambu--Jona-Lasinio model without vector correlations. It is found that the phase structure in the temperature--density plane depends sensitively on the parametrization of the model. We present two schemes of parametrization of the model where within the first one a first order phase transition from a phase with broken chiral symmetry to a color superconducting phase for temperatures below the triple point at T_t= 55 MeV occurs whereas for the second one a second order phase transition for temperatures below T_t = 7 MeV is found. In the latter case, there is also a coexistence phase of broken chiral symmetry with color superconductivity, which is a new finding within this class of models. Possible consequences for the phenomenology of the QCD phase transition at high baryon densities are discussed.
• A. Schmitt, Qun Wang, D. H. Rischke, nucl-th/0301090. Electromagnetic Meissner effect in spin-one color superconductors. It is shown that color-superconducting quark matter, where quarks of the same flavor form Cooper pairs with spin one, exhibits an electromagnetic Meissner effect. This is in contrast to spin-zero color superconductors where Cooper pairs consist of quarks with different flavors.
• I. Shovkovy, Mei Huang, hep-ph/0302142. Gapless two-flavor color superconductor. A new, gapless two-flavor color superconducting phase that appears under conditions of local charge neutrality and beta-equilibrium is revealed. In this phase, the symmetry of the ground state is the same as in the conventional two-flavor color superconductor. In the low-energy spectrum of this matter, however, there are only two gapped fermionic quasiparticles, and the rest four quasiparticles are gapless. The origin and the basic properties of the gapless two-flavor color superconductor are discussed. This phase is a natural candidate for quark matter in cores of compact star
• D. K. Hong, T. Lee, Dong-Pil Min, D. Seo, C. Song, hep-ph/0303181. Higher order corrections to Color superconducting gaps. We find a (nonlocal) gauge where the wavefunction renormalization constant does not get any corrections for all momenta in the hard-dense loop approximation. In this gauge, we solve the Schwinger-Dyson equations for the diquark condensate in dense QCD to calculate the Cooper pair gap. We determine not only the exponent but also the prefactor of the gap in a gauge independent way. We find that the higher order corrections increase the gap only by about 1.6 times to the leading order gap at Coulomb gauge. 
• T. Brauner, J. Hosek, R. Sykora, hep-ph/0303230. Color superconductor with a color-sextet condensate.We analyze color superconductivity of one massive flavor quark matter at moderate baryon density with a spin-zero color-sextet condensate. The most general Higgs-type ground-state expectation value of the order parameter implies complete breakdown of the SU(3)xU(1) symmetry. However, the lowest order calculations in both the effective bosonic description and a fermionic NJL-type model favor an enhanced SO(3) symmetry of the ground state. 
• E.Nakano, T.Maruyama, T.Tatsumi, hep-ph/0304223. Spin Polarization and Color Superconductivity in Quark Matter. A coexistent phase of spin polarization and color superconductivity in high-density QCD is investigated using a self-consistent mean-field method at zero temperature. The axial-vector current stemming from the Fock exchange term of the one-gluon-exchange interaction has a central role to cause spin polarization. The magnitude of spin polarization is determined by the coupled Schwinger-Dyson equation with a superconducting gap function. As a significant feature the Fermi surface is deformed by the axial-vector self-energy and then rotational symmetry is spontaneously broken. The gap function is also taken to be anisotropic in accordance with the deformation. As a result of numerical calculation, it is found that spin polarization barely conflicts with color superconductivity, but almost coexists with it.
• Ji-Sheng Chen, Jia-Rong Li, Peng-Fei Zhuang, nucl-th/0209043. Dispersion relation of rho meson in hot/dense nuclear matter.  The dispersion relation of $\rho$ meson in both time- and space-like regimes in hot and dense nuclear medium is analyzed and compared with $\sigma $ meson based on the quantum hadrodynamics model. The pole and screening masses of $\rho $ and $\sigma$ are discussed. The behavior of screening mass of $\rho$ is different from that of $\sigma$ due to different Dirac- and Fermi-sea contributions at finite temperature and density. 
• A. Kryjevski, hep-ph/0305173. Charge Neutrality of the Color-Flavor Locked Phase from the Low Energy Effective Theory. We investigate the issue of charge neutrality of the CFL$K^0$ phase of dense quark matter using the low energy effective theory of high density QCD. We show that the local electric and color charge neutrality of the ground state in a homogeneous color superconducting medium follows from its dynamics. We also consider the situation of a spatially inhomogeneous medium, such as may be found in a neutron star core. We find that spatial inhomogeneity results in the generation of electric fields, and positrons may be present in the ground state. We estimate the concentration of positrons in the ground state to be $n_{e^+}\sim{10^2}{cm}^{-3}$ and consider their influence on the opacity of the medium with respect to the modified photon. 
• A. Vuorinen, hep-ph/0305183. The pressure of QCD at finite temperatures and chemical potentials. The perturbative expansion of the pressure of hot QCD is computed here to order g^6ln(g) in the presence of finite quark chemical potentials. In this process all two- and three-loop one-particle irreducible vacuum diagrams of the theory are evaluated at arbitrary T and mu, and these results are then used to analytically verify the outcome of an old order g^4 calculation of Freedman and McLerran for the zero-temperature pressure. The results for the pressure and the different quark number susceptibilities at high T are compared with recent lattice simulations showing excellent agreement especially for the chemical potential dependent part of the pressure. 
• Y. Nishida, K. Fukushima, T. Hatsuda, hep-ph/0306066. Thermodynamics of strong coupling 2-color QCD with chiral and diquark condensates. 2-color QCD (quantum chromodynamics with N_c=2) at finite temperature T and chemical potential \mu is revisited in the strong coupling limit on the lattice with staggered fermions. The phase structure in the space of T, \mu, and the quark mass m is elucidated with the use of the mean field approximation and the 1/d expansion (d being the number of spatial dimensions). We put special emphasis on the interplay among the chiral condensate <\bar{q}q>, the diquark condensate <qq>, and the quark density <q^{\dagger}q> in the T-\mu-m space. Simple analytic formulae are also derived without assuming \mu nor m being small. Qualitative comparisons are made between our results and those of recent Monte-Carlo simulations in 2-color QCD. Contribution to the Hidenaga Yamagishi Commemorative volume of Physics Reports, edited by E. Witten and I. Zahed
• Hiroaki Abuki, hep-ph/0306074. Color Superconductivity in Schwinger-Dyson Approach -- Strange Quark Mass and Color-Flavor Unlocking Line --. Phase structure and phase transitions in dense QCD are studied using the Schwinger-Dyson (SD) method in the improved ladder approximation. We construct the Cornwall-Jackiw-Tomboulis (CJT) effective potentials at finite temperature for two types of pairing ansatz, namely the Color-Flavor locking (CFL) state and the two flavor superconducting (2SC) state. Strong coupling effects at low densities, such as the off-Fermi surface and antiquarks contribution to the pairing gap due to the large effective coupling, make the gap, critical temperature and those ratio deviate from those weak coupling values. Nevertheless, the ratio of the physical quantity for the CFL and that for the 2SC does not differ so much from the weak coupling value, as long as the pairing interaction is taken to be the same for the both cases. As a consequence, the CFL state always dominates over 2SC state and the critical temperatures to quark-gluon plasma (QGP) from both states coincides in the chiral limit. The energy gain in the CFL state relative to the 2SC state gets smaller towards the critical line dividing (mu, T) plane into the QGP and CFL phases, and thus small perturbations can remove the degeneracy of these critical lines. As one of such perturbations, the effect of the strange quark mass m_s on the quark-pairing is examined. In particular, using a simple kinematical criterion, we discuss the behaviour of the ``color-flavor unlocking line'' on which the CFL phase turns into the 2SC phase, against the variation of m_s. 
• Amruta Mishra, Hiranmaya Mishra, hep-ph/0306105. Chirral symmetry breaking, color superconductivity and color neutral quark matter: a variational approach. We investigate the vacuum realignment for chiral symmetry breaking and color superconductivity at finite density in Nambu-Jona-Lasinio model in a variational method. The treatment allows us to investigate simultaneous formation of condensates in quark antiquark as well as in diquark channels. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. Color and electric charge neutrality conditions are imposed through introduction of appropriate chemical potentials. Color and flavor dependent condensate functions are determined through minimisation of the thermodynamic potential. The equation of state is calculated. Simultaneous existence of a mass gap and superconducting gap is seen in a small window of quark chemical potential within the model when charge neutrality conditions are not imposed. Enforcing color and electric charge neutrality conditions gives rise to existence of gapless superconducting modes depending upon the magnitude of the gap and the difference of the chemical potentials of the condensing quarks. 
• M. Sadzikowski, hep-ph/0306114. Superconducting phase transition in the Nambu - Jona-Lasinio model. The Nambu - Bogoliubov - de Gennes method is applied to the problem of superconducting QCD. The effective quark-quark interaction is described within the framework of the Nambu - Jona-Lasinio model. The details of the phase diagram are given as a function of the strength of the quark-quark coupling constant $G^{\prime}$. It is find that there is no superconducting phase transition when one uses the relation between the coupling constants $G^{\prime}$ and $G$ of the Nambu - Jona-Lasinio model which follows from the Fierz transformation. However, for other values of $G^{\prime}$ one can find a rich phase structure containing both the chiral and the superconducting phase transitions.
• D.N. Voskresensky, nucl-th/0306077. Fluctuations of the Color-superconducting Order Parameter in Heated and Dense Quark Matter. Fluctuations of the color superconducting order parameter in dense quark matter at finite temperatures are investigated in terms of the phenomenological Ginzburg - Landau approach. Our estimates show that fluctuations of the di-quark gap may strongly affect some of thermodynamic quantities even far below and above the critical temperature. If the critical temperature of the di-quark phase transition were rather high one could expect a manifestation of fluctuations of the di-quark gap in the course of heavy ion collisions. 
• T. Schaefer, hep-ph/0307074. Hard Loops, Soft Loops, and High Density Effective Field Theory. We study several issues related to the use of effective field theories in QCD at large baryon density. We show that the power counting is complicated by the appearance of two scales inside loop integrals. Hard dense loops involve the large scale $\mu^2$ and lead to phenomena such as screening and damping at the scale $g\mu$. Soft loops only involve small scales and lead to superfluidity and non-Fermi liquid behavior at exponentially small scales. Four-fermion operators in the effective theory are suppressed by powers of $1/\mu$, but they get enhanced by hard loops. As a consequence their contribution to the pairing gap is only suppressed by powers of the coupling constant, and not powers of $1/\mu$. We determine the coefficients of four-fermion operators in the effective theory by matching quark-quark scattering amplitudes. Finally, we introduce a perturbative scheme for computing corrections to the gap parameter in the superfluid phase.
• T. D . Cohen, hep-ph/0307089. Functional integrals for QCD at nonzero chemical potential and zero density. In a Euclidean space functional integral treatment of the free energy of QCD, a chemical potential enters only through the functional determinant of the Dirac operator which for any flavor is $\dslash + m - \mu_f \gamma_0$ (where $\mu_f$ is the chemical potential for the given flavor). Any nonzero $\mu$ alters all of the eigenvalues of the Dirac operator relative to the $\mu=0$ value, leading to a naive expectation that the determinant is altered and which thereby alters the free energy. Phenomenologically, this does not occur at T=0 for sufficiently small $\mu$, in contradiction to this naive expectation. The problem of how to understand this phenomenological behavior in terms functional integrals is solved for the case of an isospin chemical through the study of the spectrum of the operator $\gamma_0 (\dslash + m)$. 
• M. Huang, I. Shovkovy, hep-ph/0307273. Gapless color superconductivity at zero and at finite temperature. We present a detailed study of the recently proposed gapless color superconductivity in neutral two-flavor quark matter in beta-equilibrium at zero as well as at finite temperature. We clarify the nature of the fermionic quasiparticles, and discuss the physical properties of this gapless phase of quark matter. The appearance of two "secondary" spin-1 condensates in the gapless ground state is pointed out. The gluon screening properties are also discussed. It is found that finite temperature properties of the gapless color superconductor are rather unusual. One of the most striking results is that the ratio of the critical temperature to the gap at zero temperature is not a universal number. Moreover, this ratio could become arbitrarily large at some values of the coupling constant. In addition, the value of the gap parameter is not a monotonic function of temperature, although the phase transition is a second order phase transition. In an extreme case, in fact, a nonzero finite temperature gap can appear even if its zero temperature value is vanishing.
  
• A.D. Jackson, F. Sannino, hep-ph/0308182. Duality in the Color Flavor Locked Spectrum. We analyze the spectrum of the massive states for the color flavor locked phase (CFL) of QCD. We show that the vector mesons have a mass of the order of the color superconductive gap $\Delta$. We also see that the excitations associated with the solitonic sector of the CFL low energy theory have a mass proportional to $F^2_{\pi}/\Delta$ and hence are expected to play no role for the physics of the CFL phase for large chemical potential. Another interesting point is that the product of the soliton mass and the vector meson mass is independent of the gap. We interpret this behavior as a form of electromagnetic duality in the sense of Montonen and Olive. Our approach for determining the properties of the massive states is non-perturbative in nature and can be applied to any theory with multiple scales.

LOFF papers





• A.M. Clogston, Upper limit for the critical field in hard superconductors. (Phys. Rev. Lett. 9 (1962) 266)
• P. Fulde and R.A. Ferrell. Superconductivity in a strong spin-exchange field.  (Phys. Rev. 135, A550, 1964)
• A.I. Larkin and Yu. N. Ovchinnikov. Inhomogeneous state of superconductors. (JETP 20, 762 (1965))
• M. R. Norman, cond-mat/9306051. Existence of the LOFF State in Superconducting UPd_2Al_3. In a recent Letter, Gloos et al have suggested that the heavy fermion superconductor, UPd_2Al_3, has a transition in magnetic field from the normal state to an inhomogeneous superconducting state, known as the LOFF state, followed at lower fields by a first order phase transition to the usual flux lattice state.
• N. Dupuis, cond-mat/9410083. Larkin-Ovchinnikov-Fulde-Ferrell state in quasi-one-dimensional superconductors. The properties of a quasi-one-dimensional (quasi-1D) superconductor with {\it an open Fermi surface} are expected to be unusual in a magnetic field. On the one hand, the quasi-1D structure of the Fermi surface strongly favors the formation of a non-uniform state Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state) in the presence of a magnetic field acting on the electron spins.
• A.I. Buzdin and H. Kachkachi, cond-mat/9611153. Generalized Ginzburg-Landau theory for non-uniform FFLO superconductors. We derive a generalized Ginzburg-Landau (GL) functional near the tricritical point in the (T,H)-phase diagram for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state, in 1,2, and 3 dimensions. (Phys. Lett. A 225 (1997) 341-348)
• H. Shimahara, cond-mat/9711017. Structure of the Fulde-Ferrell-Larkin-Ovchinnikov state in two-dimensional superconductors. Nonuniform superconducting state due to strong spin magnetism is studied in two-dimensional type-II superconductors near the second order phase transition line between the normal and the superconducting states. The optimum spatial structure of the orderparameter is examined in systems with cylindrical symmetric Fermi surfaces. It is found that states with two-dimensional structures have lower free energies than the traditional one-dimensional solutions, at low temperatures and high magnetic fields.
• A. Sedrakian and U. Lombardo, nucl-th/9907076. Thermodynamics of n-p condensate in asymmetric nuclear matter. We study the neutron-proton pairing in nuclear matter as a function of isospin asymmetry at finite temperatures and the saturation density using realistic nuclear forces and Brueckner-renormalized single particle spectra. (Phys. Rev. Lett. 84, 602 (2000))
• U. Klein, D. Rainer and H. Shimahara, cond-mat/9909124. Interplay of Fulde-Ferrell-Larkin-Ovchinnikov and Vortex states in two-dimensional Superconductors. Clean superconductors with weakly coupled conducting planes have been suggested as promising candidates for observing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We consider here a layered superconductor in a magnetic field of arbitrary orientation with respect to the conducting plane. In this case there is competition of spin-pair-breaking and orbital-pair-breaking effects.
• P. F. Bedaque, hep-ph/9910247. Color Superconductivity in Asymmetric Matter. The influence of different chemical potential for different flavors on color superconductivity is analyzed. It is found that there is a first order transition as the asymmetry grows. This transition proceeds through the formation of bubbles of low density, flavor asymmetric normal phase inside a high density, superconducting phase with a gap {\it larger} than the one found in the symmetric case. (Nucl.Phys. A697 (2002) 569-577)
• Kun Yang and D. F. Agterberg, cond-mat/9912364. Josephson Effect in Fulde-Ferrell-Larkin-Ovchinnikov Superconductors. Due to the difference in the momenta of the superconducting order parameters, the Josephson current in a Josephson junction between a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor and a conventional BCS superconductor is suppressed. (Phys. Rev. Lett. 84, 4970 (2000))
• S. Manalo,and U. Klein, cond-mat/0006327. Has the FFLO state been observed in the organic superconductor? We compare the theoretical anisotropic upper critical field $H_{C}(\Theta,T)$ of a quasi-two-dimensional d-wave superconductor with recent $H_{c2}$ data for the layered organic superconductor $\kappa-(BEDT-TTF)_2Cu(NCS)_2$. We find agreement both with regard to the angular and the temperature dependence of $H_{C}$. This supports the suggestion that the Fulde-Ferrell-Larkin-Ovchinnikov state (FFLO state) exists in this material for exactly plane-parallel orientation of the magnetic field.
• D. F. Agterberg and Kun Yang, cond-mat/0006344. Ginzburg-Landau theory of Fulde-Ferrell-Larkin-Ovchinnikov states in unconventional singlet superconductors with impurities. We derive the Ginzburg-Landau theory of unconventional singlet superconductors in the presence of a Zeeman field and impurities, in order to examine the resulting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases.(J. Phys.: Condens. Matter 13, 9259 (2001))
• R. Combescot, cond-mat/0007191. BCS superfluidity in ultracold gases with unequal atomic populations. We consider the existence of a BCS superfluid phase in $^{6}$Li due to the pairing of two hyperfine states with unequal number of atoms.(Europhys. Lett. {\bf 55}, 150 (2001))
• A. Sedrakian, nucl-th/0008052. Spatially inhomogeneous condensate in asymmetric nuclear matter. We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The quasiparticle excitation spectrum is fourfold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. (Phys.Rev. C63 (2001) 025801)
• M. G. Alford, J. A. Bowers and K. Rajagopal, hep-ph/0008208. Crystalline color superconductivity. In the case of pairing between species of    quarks with differing chemical potentials, for suitable values of the differences between chemical potentials, Cooper pairs with nonzero total momentum are favored, as was first realized by Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort spontaneously break translational and rotational invariance, leading to gaps which vary periodically in a crystalline pattern. (Phys.Rev.D63:074016,2001)
• J. A. Bowers, J. Kundu, K. Rajagopal and E. Shuster, hep-ph/0101067. A Diagrammatic approach to crystalline color superconductivity. Derivation of the gap equation through the Schwinger-Dyson equation and Nambu-Gorkov propagator. (Phys.Rev. D64 (2001) 014024)
• R. Casalbuoni, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0101326, Effective Field Theory for the Crystalline Colour Superconductive Phase of QCD. Effective lagrangian for the LOFF phase. Anisotropic dispersion relation for the phonon. (Phys.Lett. B511 (2001) 218-228)
• M. Holland, S. J. J. M. F. Kokkelmans, M. L. Chiafolo  and R. Walser, cond-mat/0103479. Resonance superfluidity in a quantum degenerate Fermi gas. We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium-40, and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5 T_F. (Phys. Rev. Lett. 87, 120406 (2001))
• A. K. Leibovich, K. Rajagopal and E. Shuster, hep-ph/0104073. Opening the crystalline color superconductivity window. The window for the LOFF phase is re-evaluated using one-gluon exchange interaction. (Phys.Rev. D64 (2001) 094005)
• J. Singleton, J.A. Symington, M.-S. Nam, A. Ardavan, M. Kurmoo and P. Day, cond-mat/0105335. Observation of the Fulde-Ferrell-Larkin-Ovchinnikov state in the quasi-two-dimensional organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$. Single crystals of the layered organic type II superconductor, $\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$, have been studied in magnetic fields of up to 33 T and at temperatures between 0.5 K and 11 K using a compact differential susceptometer. When the magnetic field lies precisely in the quasi-two-dimensional planes of the material, there is strong evidence for a phase transition from the superconducting mixed state into a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, manisfested as a change in the rigidity of the vortex system.(J. Phys. Condens. Matter Volume 12 L641 (2000))
• D.K. Hong and Y. J. Sohn, hep-ph/0107003. Critical couplings in Crystalline Color superconductivity. Solving the Schwinger-Dyson equations, we analyze the pairing of quarks in asymmetric quark matter where quarks have different chemical potentials. We show  that in the asymmetric quark matter a crystalline color-superconducting gap opens when the quark coupling is stronger than a critical value.
• R. Casalbuoni, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0107024, Effective gluon interactions in the Colour Superconductive Phase of two flavor QCD. Evaluation of the two- three- and four- point functions of the gluons in the 2SC phase. (Phys.Lett. B524 (2002) 144-152)
• F. Schreck, L. Khaykovich, K. L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles and C. Salomon, cond-mat/0107442. A quasi-pure Bose-Einstein condensate immersed in a Fermi sea. We report the observation of co-existing Bose-Einstein condensate and Fermi gas in a magnetic trap. With a very small fraction of thermal atoms, the 7Li condensate is quasi-pure and in thermal contact with a 6Li Fermi gas. The lowest common temperature is 0.28 muK = 0.2(1) T_C = 0.2(1) T_F where T_C is the BEC critical temperature and T_F the Fermi temperature. (Phys. Rev. Lett. {\bf 87}, 080403 (2001))
• K. Rajagopal, hep-ph/0109135. Crystalline Color Superconductivity. We give an introduction crystalline color superconductivity, arguing that it is likely to occur wherever quark matter in which color-flavor locking does not occur is found.(AIP Conf.Proc. 602 (2001) 339-351; Nucl.Phys. A702). (2002) 25-38)
• J. Singleton, N. Harrison, C.H. Mielke, J. Schlueter and A.M. Kini, cond-mat/0109363. A statistical model for the intrinsically broad superconducting to normal transition in quasi-two-dimensional crystalline organic metals. Although quasi-two-dimensional organic superconductors such as $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ seem to be very clean systems, with apparent quasiparticle mean-free paths of several thousand \AA, the superconducting transition is intrinsically broad (e.g $\sim 1$ K wide for $T_c \approx 10$ K). We     propose that this is due to the extreme anisotropy of these materials, which greatly exacerbates the statistical effects of spatial variations in the potential experienced by the quasiparticles.
• K. Ohwa, hep-ph/0111074. Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities. We study the possibility of spatially non-uniform ground state in (1+1)-dimensional models with quartic fermi interactions at finite fermion densities by introducing chemical potential \mu. We examine the chiral Gross-Neveu model and the Cooper pair model as toy models of the chiral symmetry breaking and the difermion pair condensates which are presumed to exist in QCD. (Phys.Rev. D65 (2002) 085040)
• G. Nardulli, hep-ph/0111178, Effective theory for QCD in the LOFF phase. Review of the LOFF phase (Copenhagen 2001, eConf C010815:104-109, 2002)
• D.K. Hong, hep-ph/0112028. Crystalline Color Superconductivity in Dense Matter. In this talk I discuss a recently proposed color superconducting phase of asymmetric quark matter where the up and down quark have different chemical potential, being in chemical equilibrium with electrons. Using Schwinger-Dyson equations derived from an effective theory of low-energy quasiparticles, a critical     coupling for LOFF phase is estimated for both the case of an effective four Fermi interaction and Landau-damped one gluon exchange. (eConf C010815 (2002) 116-124)
• T.D. Fugleberg, hep-ph/0112162. Color Superconductivity with Non-Degenerate Quarks. In dense quark matter, the response of the color superconducting gaps to a small variation, $\delta\mu$, in the chemical potential of the strange quark was studied.
• J. Kundu  and, K. Rajagopal, hep-ph/0112206.Mass induced crystalline color superconductivity. The LOFF phase is obtained by allowing a quark with non zero mass. (Phys.Rev.D65:094022,2002)
• A. M. Dyugaev, I.D. Vagner and P. Wyder, cond-mat/0112286. Nuclear ferromagnetism induced Fulde-Ferell-Larkin-Ovchinnikov state. We present a theoretical study of the influence of the nuclear ferromagnetism on superconductivity in the presence of the electron-nuclear spin interaction. It is demonstrated that in some metals, e.g. Rh, W, the BCS condensate imbedded in a matrix of ferromagneticaly ordered nuclear spins should manifest the FFLO (Fulde-Ferel-Larkin-Ovchinniov) state.
• Prashanth Jaikumar, Ralf Rapp, Ismail Zahed, hep-ph/0112308. Photon and dilepton emission rates from high density quark matter. We compute the rates of real and virtual photon (dilepton) emission from dense QCD matter in the color-flavor locked (CFL) phase, focusing on results at moderate densities (3-5 times the nuclear saturation density) and temperatures $T\simeq80$ MeV. ( Phys.Rev. C65 (2002) 055205)
• R. Casalbuoni, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0201059, Anisotropy Parameters for the Effective Description of Crystalline Color Superconductors. The parameters of the effective lagrangian describing the LOFF phase are evaluated. (Phys.Rev. D66 (2002) 014006)
• H. Won and K. Maki, cond-mat/0201124. Fulde-Ferrell-Larkin-Ovchinnikov state in d-wave superconductors. The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can be found in layered d-wave superconductors such as high $T_c$ cuprates and $\kappa$-(ET)$_2$ salts in a planar magnetic field.
• A. Serquis, X. Y. Liao, Y. T. Zhu, J. Y. Coulter, J. Y. Huang, J. O. Willis, D. E. Peterson, F. M. Mueller, N. O. Moreno, J. D. Thompson, S. S. Indrakanti andV. F. Nesterenko, cond-mat/0201486. The influence of microstructures and crystalline defects on the superconductivity of MgB2. This work studies the influence of microstructures and crystalline defects on the superconductivity of MgB2, with the objective to improve its flux pinning. (Journal of Applied Physics, Vol. 92, No. 1, pp. 351--356, 1 July 2002)
• I. Giannakis, J. T. Liu and Hai-cang Ren, hep-ph/0202138. Angular Momentum Mixing in Crystalline Color Superconductivity. In crystalline color superconductivity, quark pairs form at non-zero total momentum. This crystalline order potentially enlarges the domain of color superconductivity in cold dense quark matter. We present a perturbative calculation of the parameters governing the crystalline phase and show that this is indeed the case. Nevertheless, the enhancement is modest, and to lowest order is independent of the strength of the color interaction.
• R. Combescot and C. Mora, cond-mat/0203031. Transition to Fulde-Ferrel-Larkin-Ovchinnikov phases near the tricritical point : an    analytical study. We explore analytically the nature of the transition to the Fulde-Ferrel-Larkin-Ovchinnikov superfluid phases in the vicinity of the tricritical point, where these phases begin to appear. We make use of an expansion of the free energy up to an overall sixth order, both in order parameter amplitude and in wavevector.
• H. Shimahara, cond-mat/0203109. Fulde-Ferrell-Larkin-Ovchinnikov State and Field-Induced Superconductivity in an Organic    Superconductor.  An experimental phase diagram of the field-induced superconductivity in the lambda-(BETS)_2FeCl_4 compound is theoretically reproduced by a combination of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state and the Jaccarino-Peter mechanism.
• P. Goddard, S.W. Tozer, J. Singleton, A. Ardavan, A. Abate and M. Kurmoo, cond-mat/0203357. Superconductivity, incoherence and Anderson localization in the crystalline organic conductor. The conducting properties of the pressure-induced, layered organic superconductor (BEDT-TTF)_3Cl_2.2H_20 have been studied at 13.5 and 14.0 kbar using low temperatures, high magnetic fields and two-axis rotation.
• J. A. Bowers and K. Rajagopal, hep-ph/0204079.The crystallography of color superconductivity. Calculation of the crystalline structure minimizing the free energy in the LOFF phase
• V. Barzykin and L.P. Gor'kov, cond-mat/0204480. Inhomogeneous stripe (LOFF) phase revisited for surface superconductivity. We address 2D surface superconductivity in high magnetic fields parallel to the surface. The account for spin-orbit interaction at the surface changes properties of inhomogeneous superconducting Larkin-Ovchinnikob-Fulde-Ferrel state that develops above fields given by the paramagnetic criterion. Strong spin-orbit significantly broadens the range of existence of the LOFF phase resulting in appearance, on the surface, of periodic superconducting stripes running along the field direction.
• M.Mannarelli, hep-ph/0205098.Effective description of the LOFF phase of QCD. We present an effective field theory for the crystalline color superconductivity phase of QCD. It is kown that at high density and at low temperature QCD exhibits  a transition to a color superconducting phase characterized by energy gaps in the fermion spectra. Under specific circumstances the gap parameter has a crystalline pattern, breaking translational and rotational invariance.(Talk at the Giselda Meeting, Frascati (Roma), 14-18 Jan 2001
• Ken'ichi Takahashi, Toshiyuki Atsumi, Nariaki Yamamoto, Mingxiang Xu, Hideaki Kitazawa and Takekazu Ishida, cond-mat/0205010. Superconducting anisotropy and evidence for intrinsic pinning in single crystalline MgB$_2$. We examine the superconducting anisotropy $\gamma_c = (m_c / m_{ab})^{1/2}$ of a metallic high-$T_c$ superconductor MgB$_2$ by measuring the magnetic torque of a single crystal. The anisotropy $\gamma_c$ does not depend sensitively on the applied magnetic field at 10 K. We obtain the anisotropy parameter $\gamma_c = 4.31 \pm 0.14$.
• R. Casalbuoni, R. Gatto and G. Nardulli, hep-ph/0205219, Crystalline Color Superconductivity: Effective Lagrangian and Phonon Dispersion Law. Effective lagrangian for the cubic crystalline phase of QCD.
• M. A. Tanatar, T. Ishiguro, H. Tanaka and H. Kobayashi, cond-mat/0205239. Fulde-Ferrell-Larkin-Ovchinnikov state observed via thermal conductivity in quasi-two-dimensional organic superconductor $\lambda$-(BETS)$_2$GaCl$_4$. The thermal conductivity kappa of the quasi-two-dimensional (Q2D) organic superconductor lambda-(BETS)_2 GaCl_4 was studied in the magnetic field H applied parallel to the Q2D plane. The phase diagram determined from this bulk measurement shows notable dependence on the sample quality.
• M. Angst, R. Puzniak, A. Wisniewski, J. Roos, H. Keller and  J.Karpinski, cond-mat/0206407. Comment on "Superconducting anisotropy and evidence for intrinsic pinning in single crystalline (Comment on PRB 66, 012501 (2002) (cond-mat/0205010). In a recent paper [Phys. Rev. B 66, 012501 (2002)], torque data measured on a MgB2 single crystal in fields from 10 to 60 kOe at 10 K were presented. The  authors obtained the anisotropy gamma by fitting a theoretical expression to the data and concluded that the anisotropy is field independent gamma \approx 4.3. They also reported the observation of "intrinsic pinning", which they take as experimental evidence for the occurence of superconductivity in the boron layers. In this comment, we discuss the range of validity of the theoretical expression used by the authors and show that the conclusion of a field independent anisotropy does not hold.
• R. Casalbuoni, E. Fabiano, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0208121. Phonons and gluons in the crystalline color superconducting phase of QCD. The High Density Effective Theory formalism is used to calculate the low energy properties of the phonons and gluons in the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of two-flavor QCD. Calculations are done for the phonons of the cubic crystal and of the gluons for the cube and for the single plane wave.
• W.V. Liu and F. Wilczek, cond-mat/0208052. Interior Gap Superfluidity. We propose a new state of matter in which the pairing interactions carve out a gap within the interior of a large Fermi ball, while the exterior surface remains gapless. This defines a system which contains both a superfluid and a normal Fermi liquid simultaneously, with both gapped and gapless quasiparticle excitations. This state can be realized at weak coupling. We predict that a cold mixture of two species of fermionic atoms with different mass will exhibit this state. For electrons in appropriate solids, it would define a material that is simultaneously superconducting and metallic.
• M. Houzet, A. Buzdin, L. Bulaevskii,  M. Maley, cond-mat/0205041. New superconducting phases in field-induced organic superconductor lambbda-(BETS)2FeCl4. We derive the parallel upper critical field, Hc2, as a function of the temperature T in quasi-2D organic compound lambda-(BETS)2FeCl4, accounting for the formation of the nonuniform LOFF state. To further check the 2D LOFF model we propose to study the Hc2(T) curve at low T in tilted fields, where the vortex state is described by the high Landau level functions characterized by the index n. We predict a cascade of first order transitions between vortex phases with different n, between phases with different types of the symmetry at given n and the change of the superconducting transition from the second order to the first order as FeCl4 ions are replaced partly by GaCl4 ions.
• E. Gubankova, W. V. Liu, F. Wilczek, hep-ph/0304016. Breached pairing superfluidity: Possible realization in QCD. We propose a wide universality class of gapless superfluids, and analyze a limit that might be realized in quark matter at intermediate densities. In the breached pairing color superconducting phase heavy $s$-quarks, with a small Fermi surface, pair with light $u$ or $d$ quarks. The groundstate has a superfluid and a normal Fermi component simultaneously. We expect a second order phase transition, as a function of increasing density, from the breached pairing phase to the conventional color-flavor locked (CFL) phase. 
• C. Mora, R. Combescot, cond-mat/03065765. Nature of the Fulde-Ferrell-Larkin-Ovchinnikov phases at low temperature in 2 dimensions. We investigate, mostly analytically, the nature of the Fulde-Ferrell- Larkin-Ovchinnikov superfluid phases for an isotropic two-dimensional superconductor, which is relevant for the experimental observation of these phases. We show that there is, in the low temperature range, a cascade of transitions toward order parameters with ever increasing complexity.

Astrophysical applications





• Madappa Prakash, Ignazio Bombaci, Manju Prakash, Paul J. Ellis, James M. Lattimer and Roland Knorren, nucl-th/9603042. Composition and Structure of Protoneutron Stars. We investigate the structure of neutron stars shortly after they are born, when the entropy per baryon is of order 1 or 2 and neutrinos are trapped on dynamical timescales. (Phys.Rept. 280 (1997) 1-77)
• F. Weber and N.K. Glendenning, astro-ph/9609074. Dense Stellar Matter and Structure of Neutron Stars. After giving an overview of the history and idea of neutron stars, I shall introduce, in part one of my lectures, a representative collection of models for the equation of state of superdense neutron star matter, which account for various physical possibilities concerning the unknown behavior of such matter. Part two of my lectures deal with the construction of models of static as well as rapidly rotating neutron stars, and an investigation of the cooling behavior of such objects. (3rd Mario Schoenberg School on Physics, Joao Pessoa, Brazil, July 22 -- August 2, 1996)
• H. Heiselberg, M. Hjorth-Jensen, nucl-th/9902033. Phases of dense matter in neutron stars. Recent equations of state for dense nuclear matter are discussed with possible phase transitions arising in neutron stars such as pion, kaon and hyperon condensation, superfluidity and quark matter. (Phys. Rept. 328 (2000) 237-327)
• D. Blaschke, D. M. Sedrakian and K. M. Shahabasian, astro-ph/9904395. Diquark condensates and the magnetic field of pulsars. We study the consequences of superconducting quark cores in neutron stars for the magnetic fields of pulsars. We find that within recent nonperturbative approaches to the effective quark interaction the diquark condensate forms a superconductor of second kind whereas previously quark matter was considered as a first kind superconductor.(Astron. and Astrophys. 350, L47 (1999))
• D. Blaschke, T. Klahn and D. N. Voskresensky, astro-ph/9908334. Diquark Condensates and Compact Star Cooling. The effect of color superconductivity on the cooling of quark stars and neutron stars with large quark cores is investigated. Various known and new     quark-neutrino processes are studied. (Astrophys. J. 533, 406 (2000))
• L. Bildsten and G. Ushomirsky, astro-ph/9911155. Viscous Boundary Layer Damping of R-Modes in Neutron Stars. Recent work has raised the exciting possibility that r-modes (Rossby waves) in rotating neutron star cores might be strong gravitational wave sources. We estimate the effect of a solid crust on their viscous damping rate and show that the dissipation rate in the viscous boundary layer between the oscillating fluid and the nearly static crust is >10^5 times higher than that from the shear throughout the interior. (Astrophys. J. 529, L75 (2000))
• H. Heiselberg, nucl-th/9912002. Neutron Stars: Recent Developments. Recent developments in neutron star theory and observation are discussed. Based on modern nucleon-nucleon potentials more reliable equations of state for dense nuclear matter have been constructed. (Int.J.Mod.Phys. B15 (2001) 1519-1534)
• J. Madsen, astro-ph/9912418. Probing strange stars and color superconductivity by r-mode instabilities in millisecond pulsars. Probing strange stars and color superconductivity by r-mode instabilities in millisecond pulsars. (Phys. Rev. Lett. 85, 10 (2000) )
• B. Link, R.I. Epstein and J. M. Lattimer, astro-ph/0001245. Probing the Neutron Star Interior with Glitches. With the aim of constraining the structural properties of neutron stars and the equation of state of dense matter, we study sudden spin-ups, glitches, occurring in the Vela pulsar and in six other pulsars. (Invited talk at the Pacific Rim Conference on Stellar Astrophysics, Hong Kong, Aug. 1999. 9 pages)
• J.M. Lattimer and M. Prakash, astro-ph/0002203. Nuclear Matter and its Role in Supernovae, Neutron Stars and Compact Object Binary Mergers. The equation of state (EOS) of dense matter plays an important role in the supernova phenomenon, the structure of neutron stars, and in the mergers of compact objects (neutron stars and black holes). (Phys. Rept. 333 (2000) 121-146)
• H. Heiselberg and V. Pandharipande, astro-ph/0003276. Recent Progress in Neutron Star Theory. This review contains chapters discussing: Energy density fluctionals of nuclear matter, Many-body theory of nucleon matter, Hadronic and quark matter, Mixtures of phases in dense matter, Neutron star observations and predictions. (Ann.Rev.Nucl.Part.Sci. 50 (2000) 481-524)
• D. Page, M. Prakash, J. M. Lattimer and A. Steiner, hep-ph/0005094. Prospects of Detecting Baryon and Quark Superfluidity from Cooling Neutron Stars. Baryon and quark superfluidity in the cooling of neutron stars are investigated. Observations could constrain combinations of the neutron or Lambda-hyperon pairing gaps and the star's mass. (Phys. Rev. Lett. 85, 2048 (2000))
• S.H. Hansen, F.L. Villante, astro-ph/0005114. Decaying neutrino and a high cosmological baryon density. The low second acoustic peak in the recent Boomerang data may indicate a cosmological baryon density which is larger than allowed by standard big bang nucleosynthesis. (Phys. Lett. B486 (2000) 1-5)
• G. W. Carter and S. Reddy, hep-ph/0005228.  Neutrino Propagation In Color Superconducting Quark Matter. We calculate the neutrino mean free path in color superconducting quark matter, and employ it to study the cooling of matter via neutrino diffusion in the superconducting phase as compared to a free quark phase. (Phys. Rev. D62, 103002 (2000))
• L. Lindblom, B. J. Owen and G. Ushomirsky, astro-ph/0006242. Effect of a neutron-star crust on the r-mode instability. The presence of a viscous boundary layer under the solid crust of a neutron star dramatically increases the viscous damping rate of the fluid r-modes. We     improve previous estimates of this damping rate by including the effect of the Coriolis force on the boundary-layer eigenfunction and by using more realistic neutron-star models. (Phys.Rev. D62 (2000) 084030)
• D. Blaschke, H. Grigorian and D. N. Voskresensky, astro-ph/0009120. Cooling of Hybrid Neutron Stars and Hypothetical Self-bound Objects with Superconducting Quark Cores. We study the consequences of superconducting quark cores (with color-flavor-locked phase as representative example) for evolution of temperature profiles and the cooling curves in quark-hadron hybrid stars and in hypothetical self-bounded objects having no a hadron shell (quark core neutron stars). (Astron.Astrophys. 368 (2001) 561-568)
• D.M. Sedrakian, D. Blaschke, K.M. Shahabasyan, D.N. Voskresensky, hep-ph/0012383. Meissner effect for color superconducting quark matter. The behaviour of the magnetic field inside the superconducting quark matter core of a neutron star is investigated in the framework of the Ginzburg-Landau theory.
• R. Ouyed and F. Sannino, astro-ph/0103022. Quark Stars as inner engines for Gamma Ray Bursts? A model for Gamma ray bursts inner engine based on quark stars (speculated to exist in nature) is presented.
• David B. Kaplan, Sanjay Reddy, hep-ph/0109256. Vortices and vortons in dense quark matter. Quark matter at astrophysical densities may contain stable vortices due to the spontaneous breaking of hypercharge symmetry by kaon condensation. We argue that these vortices could be both charged and electrically superconducting. Current carrying loops (vortons) could be long lived and play a role in the magnetic and transport properties of this matter. (Phys.Rev.Lett. 88 (2002) 132302)
•  E.S. Fraga, R.D. Pisarski, J. Schaffner-Bielich, nucl-th/0110077. New Class of Compact Stars at High Density. We discuss the equation of state for cold, dense quark matter in perturbation theory, and how it might match onto that of hadronic matter. Certain choices of the renormalization scale correspond to a strongly first order chiral transition, and may generate a new class of small and very dense quark stars. (Presented at the International Conference on Statistical QCD, Bielefeld, Germany, 26-30 August 2001)
• M. Alford, hep-ph/0110150. Color superconducting quark matter in compact stars. When nuclear matter reaches a high enough density, we expect that the nucleons will overlap so much as to lose their separate identities, and merge into quark matter. In this talk I will review some theoretical expectations and speculations about quark matter, focusing on the phenomenon of quark pair condensation (color     superconductivity) and its application to compact stars. (eConf C010815 (2002) 137-148)
• Sanjay Reddy, Mariusz Sadzikowski, Motoi Tachibana, nucl-th/0203011. Neutrino Rates in Color Flavor Locked Quark Matter. We study the weak interaction rates involving Goldstone bosons in the Color Flavor Locked (CFL) quark matter. Neutrino mean free path and the rate of energy loss due to neutrino emission in a thermal plasma of CFL pions and kaons is calculated.
• Prashanth Jaikumar, Madappa Prakash and Thomas Schaefer, astro-ph/0203088. Neutrino Emission from Goldstone Modes in Dense Quark Matter. We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are $\sim 100$ MeV while the masses of Goldstone modes are on the order of 10 MeV.
• I.A. Shovkovy and P.J. Ellis, hep-ph/0204132. Thermal conductivity of dense quark matter and cooling of stars. The thermal conductivity of the color-flavor locked phase of dense quark matter is calculated. The dominant contribution to the conductivity comes from photons and Nambu-Goldstone bosons associated with breaking of baryon number which are trapped in the quark core. Because of their very large mean free path the conductivity is also very large. (Phys.Rev. C66 (2002) 015802)
• D.M. Sedrakian and D. Blaschke, hep-ph/0205107. Magnetic field of a neutron star with color superconducting quark matter core. The behaviour of the magnetic field of a neutron star with a superconducting quark matter core is investigated in the framework of the Ginzburg-Landau theory. (Astrofiz. 45 (2002) 203-212)
• I.A. Shovkovy and P.J. Ellis, astro-ph/0207346. Quark color superconductivity and the cooling of compact stars. The thermal conductivity of the color-flavor locked phase of dense quark matter is calculated. The dominant contribution to the conductivity comes from photons and Nambu-Goldstone bosons associated with the breaking of baryon number, both of which are trapped in the quark core. Because of their very large mean free path the conductivity is also very large. (Talk presented at workshop "Continuous Advances in QCD 2002/Arkadyfest," Minneapolis, USA, 17-23 May, 2002)
• M. Baldo, M. Buballa, F. Burgio, F. Neumann, M. Oertel, H.-J. Schulze, nucl-th/0212096. Neutron stars and the transition to color-superconducting quark matter. We explore the relevance of color superconductivity inside a possible quark matter core for the bulk properties of neutron stars. For the quark phase we use an Nambu--Jona-Lasinio (NJL) type model, extended to include diquark condensates. For the hadronic phase, a microscopic many-body model is adopted, with and without strangeness content. In our calculations, a sharp boundary is assumed between the hadronic and the quark phases. For NJL model parameters fitted to vacuum properties we find that no star with a pure quark core does exist. Nevertheless the presence of color superconducting phases can lower the neutron star maximum mass substantially. In some cases, the transition to quark matter occurs only if color superconductivity is present. Once the quark phase is introduced, the value of the maximum mass stays in any case below the value of two solar masses. 
• D. Blaschke, H. Grigorian, D.N. Aguilera, S. Yasui, H. Toki, hep-ph/0301087. Effects of quark matter and color superconductivity in compact stars. The equation of state for quark matter is derived for a nonlocal, chiral quark model within the mean field approximation. We investigate the effects of a variation of the form factors of the interaction on the phase diagram of quark matter under the condition of beta-equilibrium and charge neutrality. Special emphasis is on the occurrence of a diquark condensate which signals a phase transition to color superconductivity and its effects on the equation of state. We calculate the quark star configurations by solving the Tolman- Oppenheimer- Volkoff equations and obtain for the transition from a hot, normal quark matter core of a protoneutron star to a cool diquark condensed one a release of binding energy of the order of Delta M c^2 ~ 10^{53} erg. We study the consequences of antineutrino trapping in hot quark matter for quark star configurations with possible diquark condensation and discuss the claim that this energy could serve as an engine for explosive phenomena. A "phase diagram" for rotating compact stars (angular velocity-baryon mass plane) is suggested as a heuristic tool for obtaining constraints on the equation of state of QCD at high densities. It has a critical line dividing hadronic from quark core stars which is correlated with a local maximum of the moment of inertia and can thus be subject to experimental verification by observation of the rotational behavior of accreting compact stars. 
• I. Shovkovy, M. Hanauske, M. Huang, hep-ph/0303027. Nonstrange hybrid compact stars with color superconducting matter. Realistic nonstrange hybrid compact stars with color superconducting quark matter in their interior are constructed. It is shown that a positively charged two-flavor color superconducting phase could naturally appear in the core of a hybrid star as one of the components of a globally neutral mixed phase. The negatively charged normal quark phase is the other component of the mixed phase. The quark core of the star is surrounded by another mixed phase made of hadronic and normal quark matter. The two mixed phases are separated by a sharp interface. Finally, the lowest density regions of the star are made of pure hadronic matter and nuclear crust.