A Discussion on Massive Gravitons and Propagating Torsion in Arbitrary Dimensions

TL;DR

This paper reevaluates a specific $R^{2}$-type gravity model in arbitrary dimensions, incorporating torsion effects, and concludes that massive gravitons are not supported unless torsion is made propagating, which affects the model's unitarity.

Contribution

It introduces explicit torsion terms into the $R^{2}$-type gravity action and analyzes their impact on the existence of massive gravitons and unitarity across dimensions.

Findings

Ghosts and tachyons are absent only if torsion does not propagate.

The original model does not support massive gravitons.

Enlarging the model with propagating torsion could allow for massive gravitons.

Abstract

In this paper, we reassess a particular $R^{2}$-type gravity action in D dimensions, recently studied by Nakasone and Oda, taking now torsion effects into account. Considering that the vielbein and the spin connection carry independent propagating degrees of freedom, we conclude that ghosts and tachyons are absent only if torsion is non-propagating, and we also conclude that there is no room for massive gravitons. To include these excitations, we understand how to enlarge Nakasone-Oda's model by means of explicit torsion terms in the action and we discuss the unitarity of the enlarged model for arbitrary dimensions.