Effective action of gauged WZW model and exact string solutions

TL;DR

This paper develops a method to derive exact string background fields from gauged WZW models at all orders in alpha prime by using the quantum effective action and integrating out gauge fields, exemplified in the SL(2,R)/U(1) model.

Contribution

It introduces a direct field theory approach to obtain exact string solutions from gauged WZW models, matching known conformal field theory results.

Findings

Derived explicit gauge-invariant non-local effective action.

Reproduced known exact metrics and dilaton for SL(2,R)/U(1).

Provided a systematic procedure for all-order alpha prime corrections.

Abstract

We suggest how to derive the exact (all order in $\a'$) expressions for the background fields for string solutions corresponding to gauged WZW models directly at the $2d$ field theory level. One is first to replace the classical gauged WZW action by the quantum effective one and then to integrate out the gauge field. We find the explicit expression for the gauge invariant non-local effective action of the gauged WZW model. The two terms (corresponding to the group and subgroup) which appear with the same coefficients in the classical action get different $k$-dependent coefficients in the effective one. The procedure of integrating out the gauge field is considered in detail for the $SL(2,R)/U(1)$ model and the exact expressions for the $D=2$ metric and the dilaton (originally found in the conformal field theory approach) are reproduced.