CHIRAL GAUGED WESS-ZUMINO-WITTEN THEORIES AND COSET MODELS IN CONFORMAL FIELD-THEORY

The Wess Zumino-Witten (WZW) theory has a global symmetry denoted by G(L) x G(R). In the standard gauged WZW theory, vector gauge fields (i.e., with vector gauge couplings) are in the adjoint representation of the subgroup H subset-of G. In this paper, we show that, in the conformal limit in two dimensions, there is a gauged WZW theory where the gauge fields are chiral and belong to the subgroups H(L) and H(R) where H(L) and H(R) can be different groups. In the special case where H(L) = H(R), the theory is equivalent to vector gauged WZW theory. For general groups H(L) and H(R), an examination of the correlation functions (or more precisely, conformal blocks) shows that the chiral gauged WZW theory is equivalent to (G/H(L))L x (G/H(R))R coset models in conformal field theory.