On Non-Abelian Duality

TL;DR

This paper explores the theory of non-abelian duality in conformal field theories, addressing obstructions, constructing exact duals for WZW models, and extending duality concepts to anomalous subgroups and gravitational instantons.

Contribution

It provides a comprehensive framework for non-abelian duality, including exact dual constructions for WZW models and extensions to anomalous subgroups and gravitational instantons.

Findings

Identified obstructions to conformal invariance in non-semisimple groups.

Constructed exact non-abelian duals for WZW models and coset theories.

Extended duality to anomalous subgroups and applied to gravitational instantons.

Abstract

A general study of non-abelian duality is presented. We first identify a possible obstruction to the conformal invariance of the dual theory for non-semisimple groups. We construct the exact non-abelian dual for any Wess-Zumino-Witten (WZW) model for any anomaly free subgroup, and the corresponding extension for coset conformal field theories. We characterize the exact non-abelian dual for $\sigma$-models with chiral isometries and extend the standard notion of duality to anomalous subgroups of WZW models, thus giving a way of constructing dual transformations for different groups on the left and on the right. We also present some new examples of non-abelian duality for four-dimensional gravitational instantons.