Gauged WZW Models Via Equivariant Cohomology

TL;DR

This paper extends the systematic computation of gauge invariant WZW terms using equivariant cohomology from 2D to 4D, highlighting the Weil model's advantages and connections to abelian anomalies.

Contribution

It introduces the Weil model as more suitable than Cartan's for gauge invariant extensions of WZW terms in four dimensions.

Findings

Weil model better captures gauge invariance in 4D WZW extensions.

Cartan's model helps identify anomaly cancellation conditions.

Connections between equivariant cohomology and abelian anomalies are clarified.

Abstract

The problem of computing systematically the gauge invariant extension of WZW term through equivariant cohomology is addressed. The analysis done by Witten in the two-dimensional case is extended to the four-dimensional ones. While Cartan's model is used to find the anomaly cancelation condition. It is shown that the Weil model is more appropriated to find the gauge invariant extension of the WZW term. In the process we point out that Weil's and Cartan's models are also useful to stress some connections with the abelian anomaly.