Instanton and Spectral Flow in Topological Conformal Field Theories

TL;DR

This paper explores the geometric and topological aspects of 2D topological conformal field theories using gauged WZW models, revealing how instanton backgrounds induce spectral flow transformations affecting correlation functions.

Contribution

It introduces a novel interpretation of spectral flow as a singular gauge transformation within the BRST framework of topological gauged WZW models, linking instanton effects to correlation function transmutation.

Findings

Correlation functions change under different instanton backgrounds.

Spectral flow acts as a singular gauge transformation creating background charge.

Two-dimensional BF gauge theory aspects of TCFTs are elucidated.

Abstract

A class of two-dimensional topological conformal field theories (TCFTs) is studied within the framework of gauged WZW models in order to gain some insights on the global geometrical nature of TCFTs. The BRST quantizations of topological G/H gauged WZW models (the twisted versions of SUSY gauged WZW models) are given under fixed back-ground gauge fields. The BRST-cohomology of the system is investigated and the correlation functions among these physical observables are considered under the instanton back-grounds. As a consequence, two-dimensional BF gauge theoretical aspects of TCFTs are revealed. Especially it is shown that two correlation functions under the different instanton back-grounds can change to 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 back-ground charge on the physical vacuum of the system. The field identification problem of the system is also discussed from the above point of view.