A New Class of Ghost and Tachyon Free Metric Affine Gravities

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.

arXiv comment39 pages. Ancillary notebook with spin projectors is provided separately. Requires the package xTensor for Mathematica v2: references added, some minor corrections v3: corrected a mistake in the ghost-freedom condition; as a result the ghost- and tachyon-free theories are much more restricted

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