  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
$(DF)^2+F^3$ 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.
