Gravitational corrections to a non-Abelian gauge theory

TL;DR

This paper investigates the impact of gravitational corrections on non-Abelian gauge theories coupled with fermions, finding no one-loop gravitational influence on the renormalized coupling or beta function, and confirming Slavnov-Taylor identities.

Contribution

It extends previous work on gravity's effects in gauge theories by analyzing non-Abelian cases and demonstrating the absence of gravitational corrections at one-loop order.

Findings

No gravitational correction to the beta function at one-loop

Slavnov-Taylor identities are preserved at this order

Renormalized coupling remains unaffected by gravity at one-loop

Abstract

This paper is part of a series of papers exploring the renormalization of field theories coupled to gravity using the effective field theory framework. In previous works we studied the universality of the electric charge and the two-loops beta function in the Einstein-QED system. Now, we use this framework to study the non-Abelian gauge theory with fermions coupled to gravity. We show that even though some of the counterterms are dependent on the gravitational coupling, the renormalized coupling constant, and therefore the beta function, do not receive any gravitational correction at one-loop order. Also, we explicitly show that, at this order, the Slavnov-Taylor identities are respected. Finally, we end the paper putting into perspective the results of the present and the past papers.