Exact Effective Action and Spacetime Geometry in Gauged WZW Models

TL;DR

This paper derives an exact quantum effective action for gauged WZW models, capturing the full spacetime geometry including metric, dilaton, and axion fields, and analyzes geodesics in these backgrounds.

Contribution

It provides a conjectured all-orders effective action for gauged WZW models that reproduces the exact spacetime geometry from algebraic methods, including new axion field results.

Findings

Exact effective action reproduces zero mode geometry.

Axion field is non-zero at higher orders of 1/k.

Explicit solutions for geodesics in the exact geometry.

Abstract

We present an effective quantum action for the gauged WZW model $G_{-k}/H_{-k}$. It is conjectured that it is valid to all orders of the central extension $(-k)$ on the basis that it reproduces the exact spacetime geometry of the zero modes that was previously derived in the algebraic Hamiltonian formalism. Besides the metric and dilaton, the new results that follow from this approach include the exact axion field and the solution of the geodesics in the exact geometry. It is found that the axion field is generally non-zero at higher orders of $1/k$ even if it vanishes at large $k$. We work out the details in two specific coset models, one non-abelian, i.e. $SO(2,2)/SO(2,1)$ and one abelian, i.e $SL(2,\IR)\otimes SO(1,1)^{d-2}/SO(1,1)$. The simplest case $SL(2,\IR)/\IR$ corresponds to a limit.