Do the gravitational corrections to the beta functions of the quartic and Yukawa couplings have an intrinsic physical meaning?

TL;DR

This paper investigates the gauge dependence of gravitational corrections to beta functions in quantum field theories coupled to gravity, showing such corrections lack intrinsic physical meaning due to their removability via field redefinitions.

Contribution

It demonstrates that gravitational corrections to beta functions in both General and Unimodular Gravity are gauge dependent and can be eliminated by local field redefinitions, questioning their physical significance.

Findings

Gravitational corrections are gauge dependent.

Such corrections can be removed by local field redefinitions.

Claims about changes in asymptotic behavior lack intrinsic physical meaning.

Abstract

We study the beta functions of the quartic and Yukawa couplings of General Relativity and Unimodular Gravity coupled to the $\lambda\phi^4$ and Yukawa theories with masses. We show that the General Relativity corrections to those beta functions as obtained from the 1PI functional by using the standard MS multiplicative renormalization scheme of Dimensional Regularization are gauge dependent and, further, that they can be removed by a non-multiplicative, though local, field redefinition. An analogous analysis is carried out when General Relativity is replaced with Unimodular Gravity. Thus we show that any claim made about the change in the asymptotic behaviour of the quartic and Yukawa couplings made by General Relativity and Unimodular Gravity lack intrinsic physical meaning.