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⊗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⊂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⊗(G/H_R)_R coset models in conformal field theory.