On the renormalization of gauge theories in curved space-time

TL;DR

This paper demonstrates that gauge theories can be renormalized in curved space-time while preserving gauge and diffeomorphism invariance, using the BV formalism and assuming an invariant regularization.

Contribution

It establishes gauge and diffeomorphism invariant renormalizability of gauge theories in curved space-time at all loop orders, and discusses the construction of local counterterms.

Findings

Renormalization preserves gauge and diffeomorphism invariance.

Counterterms can be constructed locally on curved backgrounds.

The approach applies to general gauge theories with invariant regularization.

Abstract

We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion. Starting from this point we discuss the locality of the counterterms and the general prescription for constructing the power-counting renormalizable theories on curved background.