Non-minimal non-Abelian quantum vector fields in curved spacetime

TL;DR

This paper investigates the quantum effective action of non-minimal non-Abelian vector fields in curved spacetime, addressing gauge invariance issues and calculating one-loop divergences for various dimensions.

Contribution

It introduces a non-Abelian Stueckelberg field to handle gauge invariance breaking and derives general formulas for one-loop divergences in curved spacetime.

Findings

Ultraviolet divergences are local but non-polynomial.

Gauge invariance breaking affects only the tree level.

Explicit results provided for two-dimensional spacetime.

Abstract

The quantum effective action of non-minimal vector fields with Abelian or non-Abelian gauge degrees of freedom in curved spacetime is studied. The Proca or Yang-Mills fields are coupled to a local mass-like term acting in both coordinate and gauge spaces. Pathologies due to gauge invariance in the ultraviolet are avoided through the introduction of a non-Abelian version of the Stueckelberg field. It is found that the breaking of gauge invariance induced by the mass term affects only the tree level part of the effective action. The ultraviolet divergent part of the effective action to one loop is obtained using the method of covariant symbols and dimensional regularization. Formulas are given valid for any spacetime dimension and explicit results are shown for the two-dimensional case. As already happened for a single vector field, the ultraviolet divergences are local but not of polynomial type.