Gauged Wess-Zumino terms and Equivariant Cohomology

TL;DR

This paper explores the mathematical relationship between gauged Wess-Zumino terms in sigma-models and equivariant cohomology, providing topological criteria for when such gauging is possible.

Contribution

It establishes a one-to-one correspondence between gauged WZ-like terms and equivariant cocycles, and uses topological methods to identify conditions for the absence of obstructions.

Findings

Gauged WZ-like terms correspond to equivariant cocycles.

Obstructions to gauging relate to equivariant cohomology.

Vanishing theorems ensure gauging feasibility in certain cases.

Abstract

We summarize some results obtained on the problem of gauging the Wess--Zumino term of a d-dimensional bosonic sigma-model. We show that gauged WZ-like terms are in one-to-one correspondence with equivariant cocycles of the target space. By the same token, the obstructions to gauging a WZ term can be understood in terms of the equivariant cohomology of the target space and this allows us to use topological tools to derive some a priori vanishing theorems guaranteeing the absence of obstructions for a large class of target spaces and symmetry groups in the physically interesting dimensions d<=4. (This is an expository summary of the results of hep-th/9407149.)