Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories

TL;DR

This paper develops a field-theoretical method to derive background fields for $G/H$ coset conformal theories from gauged WZW models, providing explicit expressions and justifications for truncating non-local terms.

Contribution

It introduces a systematic approach to determine sigma model backgrounds from gauged WZW theories, including supersymmetric cases, with explicit formulas and validation against operator methods.

Findings

Derived explicit metric, dilaton, and antisymmetric tensor fields as functions of $1/k$.

Justified truncation of non-local terms in the effective action.

Showed equivalence of the metric and dilaton to operator approach results.

Abstract

We develop a field-theoretical approach to determination of the background target space fields corresponding to general $G/H$ coset conformal theories described by gauged WZW models. The basic idea is to identify the effective action of a gauged WZW theory with the effective action of a sigma model. The derivation of the quantum effective action in the gauged WZW theory is presented in detail, both in the bosonic and in the supersymmetric cases. We explain why and how one can truncate the effective action by omitting most of the non-local terms (thus providing a justification for some previous suggestions). The resulting metric, dilaton and the antisymmetric tensor are non-trivial functions of $1/k$ (or $\alpha'$) and represent a large class of conformal sigma models. The exact expressions for the fields in the sypersymmetric case are equal to the leading order (`semiclassical') bosonic expressions (with no shift of $k$). An explicit form in which we find the sigma model couplings makes it possible to prove that the metric and the dilaton are equivalent to the fields which are obtained in the operator approach, i.e. by identifying the $L_0$-operator of the conformal theory with a Klein-Gordon operator in a background. The metric can be considered as a `deformation' of an invariant metric on the coset space $G/H$ and the dilaton can be in general represented in terms of the logarithm of the ratio of the determinants of the `deformed' and `round' metrics.