On Non-Abelian Duality in Sigma Models

TL;DR

This paper introduces a new method for implementing non-Abelian duality in string sigma models, overcoming previous issues with gauge fixing and algebra closure, and ensuring a proper dual theory.

Contribution

It proposes a novel approach to non-Abelian duality that avoids algebra closure problems and improves the gauge fixing process in sigma models.

Findings

The method avoids algebra closure issues in non-Abelian duality.

It results in a consistent dual theory with proper duality properties.

The approach enlarges the isometry group to a non-semi-simple group.

Abstract

A method for implementing non-Abelian duality on string backgrounds is given. It is shown that a direct generalisation of the familiar Abelian duality induces an extra local symmetry in the gauge invariant theory. The non-Abelian isometry group is shown to be enlarged to a non-semi-simple group. However, upon eliminating the gauge fields to obtain the dual theory the new algebra does not close. Therefore the gauge fixing procedure becomes problematic. The new method proposed here avoids these issues and leads to a dual theory in the proper sense of duality.