Reassessing the foundations of Metric-Affine Gravity

TL;DR

This paper revisits the foundational aspects of Metric-Affine Gravity using the Dressing Field Method, clarifying its geometric basis and simplifying its kinematic formulation through Cartan geometry.

Contribution

It introduces a systematic gauge-invariant approach to MAG, connecting it with Cartan geometry and streamlining its kinematic description.

Findings

MAG reduces to Cartan-geometric kinematics

Dressing Field Method clarifies gauge invariance in MAG

Foundational insights into gauge translations in gravity theories

Abstract

We reassess foundational aspects of Metric-Affine Gravity (MAG) in light of the Dressing Field Method, a tool allowing to systematically build gauge-invariant field variables. To get MAG started, one has to deal with the problem of "gauge translations". We first recall that Cartan geometry is the proper mathematical foundation for gauge theories of gravity, and that this problem never arises in that framework, which still allows to clarify the geometric status of gauge translations. Then, we show how the MAG kinematics is obtained via dressing in a technically streamlined way, which highlights that it reduces to a Cartan-geometric kinematics.