Conformal Gravity and Extensions of Critical Gravity

TL;DR

This paper explores conformal and critical gravity theories involving Weyl-squared actions, connecting different approaches, generalizing to wider classes, and extending to six dimensions, with implications for ghost mode elimination and boundary conditions.

Contribution

It establishes connections between critical gravity and Weyl-squared modifications, generalizes critical gravity to new models, and constructs six-dimensional conformal and non-conformal gravities.

Findings

Weyl-squared actions relate critical gravity and Maldacena's approach.

Ghostlike spin-2 modes can be eliminated via boundary conditions.

Constructed conformal and non-conformal gravities in six dimensions.

Abstract

Higher-order curvature corrections involving the conformally-invariant Weyl-squared action have played a role in two recent investigations of four-dimensional gravity; in critical gravity, where it is added to the standard cosmological Einstein-Hilbert action with a coefficient tuned to make the massive ghostlike spin-2 excitations massless, and in a pure Weyl-squared action considered by Maldacena, where the massive spin-2 modes are removed by the imposition of boundary conditions. We exhibit the connections between the two approaches, and we also generalise critical gravity to a wider class of Weyl-squared modifications to cosmological Einstein gravity where one can eliminate the massive ghostlike spin-2 modes by means of boundary conditions. The cosmological constant plays a crucial role in the discussion, since there is then a "window" of negative mass-squared spin-2 modes around AdS_4 that are not tachyonic. We also construct analogous conformal and non-conformal gravities in six dimensions.