Non-Abelian Duality Based on Non-Semi-Simple Isometry Groups

TL;DR

This paper investigates non-Abelian duality transformations for sigma models with non-semi-simple isometry groups, establishing conditions for their equivalence and demonstrating conformal invariance in specific cases.

Contribution

It provides the first detailed analysis of non-Abelian duality for non-semi-simple groups, including conditions for model equivalence and conformal invariance.

Findings

Conditions for equivalence of original and dual models

Construction of conformally invariant dual models

Resolution of conformal invariance obstructions

Abstract

Non-Abelian duality transformations built on non-semi-simple isometry groups are analysed. We first give the conditions under which the original non-linear sigma model and its non-Abelian dual are equivalent. The existence of an invariant and non-degenerate bilinear form for the isometry Lie algebra is crucial for this equivalence. The non-Abelian dual of a conformally invariant sigma model, with non-semi-simple isometries, is then constructed and its beta functions are shown to vanish. This study resolves an apparent obstruction to the conformal invariance of sigma models obtained via non-Abelian duality based on non-semi-simple groups.