Topological Gauged WZW Models and 2D Gravity

TL;DR

This paper explores a topological gauged WZW model related to SU(2)/U(1), revealing its equivalence to a topological conformal field theory with dual algebraic structures and its reduction to various formulations of 2D gravity.

Contribution

It introduces a novel topological gauged WZW model framework that unifies multiple 2D gravity theories through different gauge choices.

Findings

Model is equivalent to a topological conformal field theory with two algebraic structures.

Formalism reduces to K.Li's, KPZ, and DDK (Liouville) theories under specific gauge choices.

Provides a unified topological approach to 2D gravity coupled with conformal matter.

Abstract

We study the "topological gauged WZW model associated with $SU(2)/U(1)$",which is defined as the twisted version of the corresponding supersymmetric gauged WZW model. It is shown that this model is equivalent to a topological conformal field theory characterized by two independent topological conformal algebras, one of which is the "twisted Kazama-Suzuki type" and the other is "twisted Coulomb gas type". We further show that our formalism of this gauged WZW model naturally reduces to the well-known formulations of 2D gravity coupled with conformal matter; one of the gauge choices leads to the K.Li's theory, and the alternative choices lead to the KPZ theory or the DDK (Liouville) theory.