A Gauge Theoretic Approach to Gravity

TL;DR

This paper reformulates General Relativity as an SU(2) gauge theory, simplifying the linearized graviton description, revealing a broader class of gravity theories, and exploring implications for matter coupling and quantum gravity UV completion.

Contribution

It introduces a gauge theoretic formulation of GR, demonstrating its advantages and the existence of multiple gravity theories beyond standard GR.

Findings

Linearized graviton Lagrangian is simpler and convex in gauge form.

Full non-linear theory is equivalent to GR on-shell.

Multiple gravity theories exist with two graviton polarizations.

Abstract

Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full non-linear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an inifnite-parameter class of gravity theories all describing just two propagating polarisations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang-Mills arise as sectors of a general diffeomorphism invariant gauge theory. We finish by outlining a possible scenario of the UV completion of quantum gravity within this approach.