Self-dual 6d 2-form fields coupled to non-abelian gauge field: quantum corrections

We study a 6d model of a set of self-dual 2-form B-fields interacting with a non-abelian vector A-field which is restricted to a 5d subspace. One motivation is that if the gauge vector could be expressed in terms of the B-field or integrated out, this model could lead to an interacting theory of B-fields only. Treating the 5d gauge vector as a background field, we compute the divergent part of the corresponding one-loop effective action which has the (DF)² + F³ structure and compare it with similar contributions from other 6d fields. We also discuss a 4d analog of the non-abelian self-dual model, which turns out to be UV finite.