Seeing a c-theorem with holography

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.

Figures (1)

• Figure 1: A slice of constant $t$ through the AdS$_{d+1}$ metric in eq. (\ref{['metric1']}). This slice bears some similarity to the Einstein-Rosen bridge in a Schwarzschild black hole HE. Note that only half of the AdS boundary is reached in the limit $r\rightarrow\infty$. The other half is reached from the second asymptotic region 'behind the horizon'.