On unitarity of a Yang-Mills type formulation for massless and massive gravity with propagating torsion

TL;DR

This paper investigates the unitarity of a Yang-Mills formulation of gravity with propagating torsion, analyzing massless and massive cases, and identifies conditions for unitary theories consistent with Einstein's solutions.

Contribution

It introduces a Yang-Mills gravity model with torsion, demonstrating conditions for unitarity in both massless and massive regimes, and extends the theory to include parity-preserving quadratic torsion terms.

Findings

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

Massive extension reproduces a unitary Hilbert-Einstein-Fierz-Pauli theory plus additional modes.

Existence of a family of unitary Yang-Mills-extended theories compatible with Einstein solutions.

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. Finally we confirm the existence of a family of unitary Yang-Mills-extended theories which are classically consistent with Einstein's solutions coming from non massive and topologically massive gravity.