Gravity as a diffeomorphism invariant gauge theory

TL;DR

This paper presents a formulation of gravity as a diffeomorphism invariant SU(2) gauge theory, detailing its linearized structure, gauge fixing, and propagator, with implications for quantum gravity.

Contribution

It develops a gauge-theoretic description of gravity that simplifies the propagator and removes the Planck length as a fundamental scale, aiding quantization efforts.

Findings

Propagator resembles Yang-Mills with a diffeomorphism projector

Gravity described as an SU(2) gauge theory with two graviton polarizations

Planck length is not fundamental in this formulation

Abstract

A general diffeomorphism invariant SU(2) gauge theory is a gravity theory with two propagating polarizations of the graviton. We develop this description of gravity, in particular for future applications to the perturbative quantization. Thus, the linearized theory, gauge symmetries, gauge fixing are discussed in detail, and the propagator is obtained. The propagator takes a simple form of that of Yang-Mills theory with an additional projector on diffeomorphism equivalence classes of connections inserted. In our approach the gravitational perturbation theory takes a rather unusual form in that the Planck length is no longer fundamental.