Gauged Wess-Zumino terms and equivariant cohomology

We summarize some results obtained on the problem of gauging the Wess-Zumino term of a d-dimensional bosonic σ-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.