Parafermionic Reductions of WZW Model

J. F. Gomes; G. M. Sotkov; A. H. Zimerman

paper

Parafermionic Reductions of WZW Model

arXiv:hep-th/9803234

Abstract

We investigate a class of conformal Non-Abelian-Toda models representing a noncompact $S L (2, R) / U (1)$ parafermionions (PF) interacting with a specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras and the exact solution of these models is presented. An important property of this class of models is the affine $S L (2, R)_{q}$ algebra spanned by charges of the chiral and antichiral nonlocal currents and the U(1) charge. The classical (Poisson Brackets) algebras of symmetries $V G_{n}$ of these models appears to be of mixed PF- $W G_{n}$ type. They contain together with the local quadratic terms specific for the $W_{n}$ -algebras the nonlocal terms similar to the ones of the classical PF-algebra. The renormalization of the spins of the nonlocal currents is the main new feature of the quantum $V A_{n}$ -algebras. The quantum $V A_{2}$ -algebra and its degenerate representations are studied in detail.

63 pages, latex file (run twice)