Holographic c-theorems in arbitrary dimensions

TL;DR

This paper demonstrates that holographic c-theorems hold in higher curvature gravity theories across arbitrary dimensions, linking flow quantities to central charges and entanglement entropy coefficients, and proposes a new c-theorem for odd-dimensional CFTs.

Contribution

It introduces a method to select gravity theories that obey holographic c-theorems and identifies entanglement entropy coefficients as central charges in odd dimensions.

Findings

Holographic c-theorem applies to higher curvature gravity theories.

In even dimensions, the flow quantity is the A-type trace anomaly central charge.

Entanglement entropy coefficients serve as central charges in odd-dimensional CFTs.

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.