Equivalent models for gauged WZW theory

TL;DR

This paper modifies the $SL(2,{f R})/U(1)$ WZW theory to include chiral $U(1)$ gauge invariance, revealing connections to Liouville theory and black hole physics, and discusses the physical state structure.

Contribution

It introduces a gauge-invariant formulation of the gauged WZW model using a Stueckelberg field and explores its reduction to Liouville theory under specific gauge conditions.

Findings

The gauge-invariant model is equivalent to a Liouville theory coupled to $c=1$ matter.

Certain gauge choices simplify the model to known 2D black hole descriptions.

Discussion of physical states provides insight into the spectrum of the theory.

Abstract

We modify the $SL(2,{\bf R})/U(1)$ WZW theory, which was shown to describe strings in a 2D black hole, to be invariant under chiral $U(1)$ gauge symmetry by introducing a Steukelberg field. We impose several interesting gauge conditions for the chiral $U(1)$ symmetry. In a paticular gauge the theory is found to be reduced to the Liouville theory coupled to the $c=1$ matter perturbed by the so-called black hole mass operator. Also we discuss the physical states in the models briefly.