Instanton and spectral flow in topological conformal field theories

Abstract

A class of two-dimensional topological conformal field theories (TCFTs) is studied within the framework of gauged WZW models in order to obtain some insights on the global geometrical nature of TCFTs. The BRST quantizations of topological G/H gauged WZW models (the twisted versions of supersymmetric gauged WZW models) are given under fixed background gauge fields. The BRST cohomology of the system is investigated, and then the correlation functions among these physical observables are considered under the instanton backgrounds. As a consequences, two-dimensional BF gauge theoretical aspects of TCFTs are revealed. Especially, it is shown that two correlatation functions under the different instanton backgrounds can change into each other. This process of transmutation is described by the spectral flow. The flow is formulated as a “singular” gauge transformation which creates an appropriate background charge on the physical vacuum of the system. The field identification problem of the system is also discussed from the above point of view.