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

TL;DR

This paper investigates a 6-dimensional model of self-dual 2-form fields coupled to a non-abelian gauge field, analyzing quantum corrections and potential for an interacting B-field theory, with implications for UV finiteness in related 4d models.

Contribution

It computes the one-loop divergences of a 6d self-dual 2-form coupled to a non-abelian gauge field and explores a UV-finite 4d analog of the model.

Findings

The divergence has a (DF)^2 + F^3 structure.

The 4d analog of the model is UV finite.

Comparison with other 6d fields' contributions.

Abstract

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.