On the renormalization of Metric-Affine Gravity theories

TL;DR

This paper investigates the renormalization properties of Metric-Affine Gravity theories with torsion and nonmetricity, providing explicit one-loop divergence calculations and correcting previous results on beta functions.

Contribution

It offers the first detailed one-loop divergence analysis for a class of Metric-Affine Gravity theories with independent metric and connection, correcting prior beta function calculations.

Findings

Explicit one-loop divergences computed for theories with torsion and nonmetricity

Correction of the known beta function for the Yang--Mills term in this context

Identification of additional terms generated during renormalization

Abstract

We discuss the renormalization group in the context of gravitational theories with independent metric and affine connection. Considering a class of theories with both propagating torsion and nonmetricity, we perform an explicit computation of one-loop divergences, starting from a simple yet phenomenologically viable modification of the Yang--Mills-like action. Similarly to what happens in Poincar\'e gauge theory, in addition to the action, quadratic in curvature, torsion, and nonmetricity, many more terms are generated. We correct a known result for the beta function of the Yang--Mills term and show that considerations previously presented in the literature are incomplete.