Seeing a c-theorem with holography

TL;DR

This paper explores holographic RG flows with higher curvature gravity, revealing that the central charge 'a' decreases monotonically while 'c' does not, and proposes a new c-theorem based on entanglement entropy in arbitrary dimensions.

Contribution

It introduces a holographic model with higher curvature terms that distinguishes the flow of central charges 'a' and 'c', and formulates a new c-theorem applicable in any dimension.

Findings

Central charge 'a' exhibits monotonic flow in holographic RGs.

Central charge 'c' does not necessarily decrease along RG flows.

A new c-theorem based on entanglement entropy is proposed for arbitrary dimensions.

Abstract

There is no known model in holography exhibiting a $c$-theorem where the central charges of the dual CFT are distinct. We examine a holographic model of RG flows in a framework where the bulk gravity theory contains higher curvature terms. The latter allows us to distinguish the flow of the central charges $a$ and $c$ in the dual field theories in four dimensions. One finds that the flow of $a$ is naturally monotonic but that of $c$ is not. Extending the analysis of holographic RG flows to higher dimensions, we are led to formulate a novel c-theorem in arbitrary dimensions for a universal coefficient appearing in the entanglement entropy of the fixed point CFT's.