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 six-parameter class of theories that are projective invariant, contain only one massless spin 2 and no spin 3, and are free of ghosts and tachyons.
Highlights
Metric-affine gravity (MAG) is a broad class of theories of gravity based on an independent metric and connection
More attention has been given to theories with torsion, but recently, there has been a great deal of interest for MAGs with nonmetricity; see, e.g., Refs. [3,4,5,6,7,8,9,10,11,12,13]
The main reason for our interest in MAG is its relation to quadratic gravity1 and its similarity to gauge theories of the fundamental interactions
Summary
Metric-affine gravity (MAG) is a broad class of theories of gravity based on an independent metric (or tetrad) and connection. The most general ghost and tachyon-free theories not containing accidental symmetries have been determined in Refs. The purpose of this paper is to give the tools that are necessary to address this problem for general MAG, containing both torsion and nonmetricity, and to exhibit a new class of ghost- and tachyon-free theories with nonmetricity. We determine the spin projection operators for the fields that appear in the linearized action, which facilitate the inversion of the wave operator to obtain the propagator for each spin sector We specialize these results to the case of theories with metric or torsion-free connections. We determine a six-parameter family of theories that are ghost and tachyon free, propagating a massless graviton and massive spin-2−, -1þ, and -1− states with distinct masses
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