# WEB page for the paper esi/828

## Coset Construction of Parafermionic Hall States

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