On the general structure of gauged Wess – Zumino – Witten terms

The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H ⊂ G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and a general expression for these cocycles is given. Their formal similarity with the expressions recently found for other related problems (effective actions of WZW type) is also discussed and explained.