Topological gauged WZW model and two-dimensional gravity

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 the “twisted Coulomb gas type”. We further show that our formalism of this gauged WZW model naturally reduces to the well-known formulations of two-dimensional gravity coupled with conformal matter; one of the gauge choices leads to Li's theory, and the alternative choices lead to the KPZ theory or the DDK (Liouville) theory. In the appendix we argue on a possibility of deriving such topological conformal models from the G/G-gauged WZW models.