Non-abelian anomalies and effective actions for a homogeneous space G/H

We consider the problem of constructing the fully gauged effective action in 2n-dimensional space-time for Nambu-Goldstone bosons valued in a homogeneous space G/H, with the requirement that the action is a solution of the anomalous Ward identity and that it is invariant under the gauge transformations of H. We show that this can be done whenever the homotopy group pi(2n)(G/H) is trivial, G/H is reductive and H is embedded in G so as to be anomaly free, in particular when H is an anomaly safe group. We construct the necessary generalization of the Bardeen counterterm and give explicit forms for the anomaly and the effective action. When G/H is a symmetric space, the counterterm and the anomaly decompose into a parity-even and a parity-odd part. In this case, for the parity-even part of the action, one does not need the anomaly free embedding of H.