Semi-invariant terms for gauged non-linear sigma-models

We determine all the terms that are gauge-invariant up to a total spacetime derivative ("semi-invariant terms") for gauged non-linear sigma models. As suming that the isotropy subgroup H of the gauge group is compact or semi-s imple, we show that (non-trivial) such terms exist only in odd dimensions a nd are equivalent to the familiar Chem-Simons terms for the subgroup H. Var ious applications are mentioned, including one to the gauging of the Wess-Z umino-Witten terms in even spacetime dimensions. Our approach is based on t he analysis of the descent equation associated with semi-invariant terms. ( C) 2000 Elsevier Science B.V. All rights reserved.