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

TL;DR

This paper investigates the unitarity of a Yang-Mills formulation of gravity with torsion in 2+1 dimensions, identifying conditions for unitary massive and massless modes and proposing classically consistent extensions.

Contribution

It introduces a Yang-Mills gravity model with torsion, analyzes its unitarity, and identifies a family of classically consistent, perturbatively unitary extended theories.

Findings

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

Massive theory reproduces a unitary Fierz-Pauli-like model plus non-unitary modes.

A family of unitary Yang-Mills-extended theories consistent with Einstein solutions is confirmed.

Abstract

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang-Mills formulation for gravity in a $2+1$ dimensional space-time. In the massless case we show that the theory contains 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 represents 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. The unitarity of these YM-extended theories is shown in a perturbative regime. A possible way to perform a non-perturbative study is remarked.