Semi-Invariant Terms for Gauged Non-Linear Sigma-Models

TL;DR

This paper classifies gauge-invariant terms, known as semi-invariant terms, in gauged non-linear sigma models, revealing their equivalence to Chern-Simons terms in odd dimensions and discussing applications like Wess-Zumino-Witten term gauging.

Contribution

It provides a complete classification of semi-invariant terms in gauged non-linear sigma models, linking them to Chern-Simons terms and analyzing their existence conditions.

Findings

Semi-invariant terms exist only in odd dimensions.

Such terms are equivalent to Chern-Simons terms for the subgroup H.

Applications include gauging Wess-Zumino-Witten terms.

Abstract

We determine all the terms that are gauge-invariant up to a total spacetime derivative ("semi-invariant terms") for gauged non-linear sigma models. Assuming that the isotropy subgroup $H$ of the gauge group is compact or semi-simple, we show that (non-trivial) such terms exist only in odd dimensions and are equivalent to the familiar Chern-Simons terms for the subgroup $H$. Various applications are mentioned, including one to the gauging of the Wess-Zumino-Witten terms in even spacetime dimensions. Our approach is based on the analysis of the descent equation associated with semi-invariant terms.