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WEB page for the paper esi/828

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Coset Construction of Parafermionic Hall States

**Authors:** A. Cappelli,
L.
S. Georgiev, I. T. Todorov

**Comments:** Latex, 15 pages

**Report-no:** preprint ESI 828 (2000)

**Subj-class**: High Energy Physics - Theory; Mesoscopic Systems
and Quantum Hall Effect;Mathematical Physics

**Journal-ref**: Proceedings of ``Supersymmetries and Quantum
Symmetries'', SQS'99, July 1999, Dubna, and of
the ``6th Wigner Symposium'', Istambul, August 1999
Fractional quantum Hall fluids with fillings 2 < \nu <3
have been recently proposed which
generalize the Pfaffian state into a hierarchy of
states with parafermionic excitations.
We describe here the corresponding Z_k-parafermion conformal
field theory by means of the coset construction
(su(k)_1 + su(k)_1)/su(k)_2.
This extends our earlier derivation of the Pfaffian state
from a ``parent'' state with abelian affine symmetry plus a
projection of degrees of freedom.
The numerator of the coset
is actually a rational conformal field theory made out of
(2k-2) scalar fields and a specific extended symmetry.
The coset construction projects out some neutral Hall edge excitations
while preserving the filling fraction; it also respects the Z_k parity rule
coupling neutral and charged excitations in the parent abelian theory.