Local BRST cohomology of the gauged principal non-linear sigma model

TL;DR

This paper computes the local BRST cohomology for gauged non-linear sigma models on group manifolds, providing insights into gauging WZW terms and topological actions, applicable to both dynamical and topological gauge fields.

Contribution

It offers a comprehensive calculation of BRST cohomology for gauged sigma models on any Lie group, clarifying the structure of topological terms and symmetries.

Findings

Cohomology results for dynamical gauge fields

Cohomology results for topological G/G models

Recovery of known effective action classifications

Abstract

The local BRST cohomology of the gauged non-linear sigma model on a group manifold is worked out for any Lie group G. We consider both, the case where the gauge field is dynamical and the case where it has no kinetic term (G/G topological theory). Our results shed a novel light on the problem of gauging the WZW term as well as on the nature of the topological terms introduced a few years ago by De Wit, Hull and Rocek. We also consider the BRST cohomology of the rigid symmetries of the ungauged model and recover the results of D'Hoker and Weinberg on the most general effective actions compatible with the symmetries.