Critical Points of D-Dimensional Extended Gravities

TL;DR

This work analyzes a D-dimensional gravity theory augmented by quadratic curvature terms and identifies a rich structure of vacua and linearized excitations. By tuning the parameters, the authors uncover a critical point in which one AdS vacuum supports only massless spin-2 modes and all excitations have zero energy, while scalar modes can be suppressed via a specific constraint. They derive the conserved charges using the Deser–Tekin formalism and show that at criticality the energy of asymptotically AdS black holes vanishes. The linear spectrum features a product of second-order operators yielding massless and massive spin-2 modes, with the massive branch becoming massless at the critical point, resulting in a theory with vanishing excitation energies. Special reductions reproduce known theories in lower dimensions, and in higher dimensions a Weyl-squared limit provides a one-parameter model with a single AdS vacuum, highlighting a path to unitary, higher-dimensional gravity at criticality.

Abstract

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, whose Λis determined.