On the renormalization of Poincar\'e gauge theories

TL;DR

This paper performs a one-loop analysis of Poincaré Gauge Theories, revealing that they generate additional terms upon renormalization, and concludes that such models are generally non-renormalizable due to the emergence of new curvature terms.

Contribution

It provides an explicit one-loop calculation for Poincaré Gauge Theories, showing the generation of new terms and analyzing their impact on renormalizability.

Findings

All terms except those with torsion are generated and can be eliminated by field redefinitions.

A new quadratic curvature term appears, rendering the model non-renormalizable.

The behavior of more general theories of this type is discussed.

Abstract

Poincar\'e Gauge Theories are a class of Metric-Affine Gravity theories with a metric-compatible (i.e. Lorentz) connection and with an action quadratic in curvature and torsion. We perform an explicit one-loop calculation starting with a single term of each type and show that not only are all other terms generated, but also many others. In our particular model all terms containing torsion are redundant and can be eliminated by field redefinitions, but there remains a new term quadratic in curvature, making the model non-renormalizable. We discuss the likely behavior of more general theories of this type.