Conformal Gravity and Extensions of Critical Gravity

TL;DR

The paper develops higher-derivative gravity theories built from Weyl-squared and related conformal invariants in $D=4$ and $D=6$, showing that ghostlike massive spin-2 modes can be consistently truncated by AdS boundary conditions to yield a unitary massless graviton and an effective equivalence to Einstein gravity in the infrared. It introduces a 1-parameter family of 4D theories with non-tachyonic negative $M^2$ massive modes that are removable at infinity, broadening the space of potentially renormalizable models and enabling nontrivial UV fixed points. The authors extend the construction to 6D, where a similar Einstein/conformal duality persists, and identify critical and tri-critical points controlling the higher-derivative dynamics. The results suggest a renormalization-group path from finite higher-derivative theories to conformal gravity at high energies, offering a framework in which renormalizability and infrared Einstein gravity can coexist. Overall, the work extends the landscape of ghost-free higher-derivative gravities and clarifies how boundary conditions can enforce physically viable spectra while preserving long-wavelength Einstein physics.

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.