Holographic c-theorems in arbitrary dimensions

TL;DR

The paper extends the holographic c-theorem framework beyond Einstein gravity to higher-curvature bulk theories, introducing a monotone a_d^* that governs RG flows. It shows that for even boundary dimensions, a_d^* precisely equals the A-type central charge A and is tied to a universal entanglement-entropy contribution, while for odd dimensions it remains interpretable via entanglement measures. By imposing unitarity constraints and analyzing conical defects, AdS equations of motion, and Wald entropy, the authors establish a consistent holographic picture in which a_d^* counts boundary degrees of freedom and obeys a monotonic flow. They also distinguish a_d^* from other proposed central charges, argue for a Cardy-like c-theorem in odd dimensions, and discuss broader implications for holography and entanglement in higher dimensions.

Abstract

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.