Chiral Gauged WZW Theories and Coset Models in Conformal Field Theory

TL;DR

This paper introduces a chiral gauged WZW theory in two dimensions, showing its equivalence to certain coset models and extending the understanding of gauge symmetries in conformal field theory.

Contribution

It demonstrates that chiral gauged WZW theories with different left and right subgroups are equivalent to specific coset models, generalizing the standard vector gauged WZW theory.

Findings

Chiral gauged WZW theories correspond to $(G/H)_L imes (G/H)_R$ coset models.

Vector gauged WZW theory is a special case where $H_L=H_R$.

Correlation functions confirm the equivalence between chiral gauged WZW and coset models.

Abstract

The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by $G_L\otimes G_R$. In the standard gauged WZW theory, vector gauge fields (\ie\ with vector gauge couplings) are in the adjoint representation of the subgroup $H \subset G$. 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 $(G/H)_L\otimes (G/H)_R$ coset models in conformal field theory. The equivalence of the vector gauged WZW theory and the corresponding $G/H$ coset theory then follows.