On Conformal Properties of the Dualized Sigma-Models

TL;DR

This paper investigates how non-abelian duality affects the conformal invariance of sigma-models, revealing conditions under which conformality is preserved or broken, with specific examples illustrating these effects.

Contribution

It provides the first calculation of first-order beta-functions for dualized sigma-models with dilaton, highlighting when conformal invariance is maintained or violated.

Findings

Non-abelian duality preserves conformality for semi-simple groups.

An extra beta-function contribution arises proportional to the trace of structure constants.

Examples include Bianchi V cosmology and G  G WZW model.

Abstract

We have calculated the first-order beta-functions for a sigma-model ( with dilaton) dualized with respect to an arbitrary Lie group that acts without isotropy. We find that non-abelian duality preserves conformal invariance for semi-simple groups, but in general there is an extra contribution to the beta-function proportional to the trace of the structure constants, which cannot be absorbed into an additional dilaton shift. Two particular examples, a Bianchi V cosmological background and the G \otimes G WZW model, are discussed.