Gauss Decomposition, Wakimoto Realisation and Gauged WZNW Models

TL;DR

This paper investigates a novel approach to gauging WZNW models via Gauss decomposition, revealing differences from standard methods and connecting it to Wakimoto variables, with implications for the model's geometric interpretation.

Contribution

It introduces a new gauging method using Gauss decomposition, showing its unique features and relation to Wakimoto variables, contrasting with traditional gauging approaches.

Findings

Gauging via Gauss decomposition involves minimal coupling to gauge fields.

Gauging an abelian vector subgroup differs from standard gauging by field strength terms.

The resulting target-space metric is degenerate, lacking a sigma model interpretation.

Abstract

The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging an abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables.