A New Class of Ghost and Tachyon Free Metric Affine Gravities

TL;DR

This paper develops a framework for analyzing metric-affine gravity theories, identifying a broad class free of ghosts and tachyons, with potential implications for consistent quantum gravity models.

Contribution

It introduces spin-projection operators for complex tensor fields and characterizes the most general ghost- and tachyon-free, projective-invariant metric-affine gravity theories with a massless spin 2.

Findings

Identifies a class of ghost- and tachyon-free theories

Provides explicit spin-projection operators for tensor analysis

Recovers known results in the metric case

Abstract

We construct the spin-projection operators for a theory containing a symmetric two-index tensor and a general three-index tensor. We then use them to analyse, at linearized level, the most general action for a metric-affine theory of gravity with terms up to second order in curvature, which depends on 28 parameters. In the metric case we recover known results. In the torsion-free case, we are able to determine the most general class of theories that are projective invariant, contain only one massless spin 2 and no spin 3, and are free of ghosts and tachyons.