On the renormalization of Metric-Affine Gravity theories

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.