Non-consistency of a pure Yang-Mills type formulation for gravity revisited

TL;DR

This paper investigates a pure Yang-Mills formulation of gravity with a focus on contorsion and metric background, revealing issues with unitarity and the propagation of degrees of freedom in both massless and massive cases.

Contribution

It revisits the pure Yang-Mills approach to gravity, analyzing its degrees of freedom and unitarity, and introduces quadratic torsion terms to explore massive extensions.

Findings

Massless case propagates three degrees of freedom with one non-unitary mode.

Quadratic torsion terms yield a unitary massive theory plus additional modes.

The theory exhibits non-unitarity issues in both massless and massive regimes.

Abstract

A perturbative regime based on contorsion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang-Mills formulation based on $GL(3,R)$ gauge group. In the massless case we show that the theory propagates three degrees of freedom and only one is a non-unitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert-Einstein-Fierz-Pauli unitary massive theory plus three massless modes, two of them non-unitary ones.