Holographic c-theorems and higher derivative gravity

TL;DR

This paper proves a holographic c-theorem for Lovelock gravity, a higher curvature theory with second-order equations, and explores conditions for monotonicity in f(R) gravity, highlighting differences in entropy laws.

Contribution

It establishes a holographic c-theorem for Lovelock gravity and analyzes the conditions needed for monotonic flows in f(R) gravity, extending the understanding of holographic RG flows.

Findings

Proved a c-theorem for Lovelock gravity with second-order equations.

Identified additional conditions for monotonicity in f(R) gravity.

Compared entropy laws in f(R) gravity with second law implications.

Abstract

In AdS/CFT, the holographic Weyl anomaly computation relates the a-anomaly coefficient to the properties of the bulk action at the UV fixed point. This universal behavior suggests the possibility of a holographic c-theorem for the a-anomaly under flows to the IR. We prove such a c-theorem for higher curvature Lovelock gravity, where the bulk equations of motion remain second order. We also explore f(R) gravity as a toy model where higher derivatives cannot be avoided. In this case, monoticity of the flow requires an additional condition related to the higher derivative nature of the theory. This is in contrast to the case of f(R) black hole entropy, where the second law follows from application of the full Einstein equations and the null energy condition.