RG Flow and Thermodynamics of Causal Horizons in Higher-Derivative AdS Gravity

TL;DR

This paper verifies that the second law of thermodynamics for causal horizons in higher-derivative AdS gravity theories acts as a holographic c-theorem, extending previous results beyond Einstein gravity.

Contribution

It demonstrates that the second law of causal horizon thermodynamics ensures a holographic c-theorem in higher-derivative gravity theories, including those with curvature-matter couplings.

Findings

Entropy density on causal horizons acts as a holographic c-function.

A sufficient condition for the holographic c-theorem is the second law of causal horizon thermodynamics.

Conjecture that all unitary higher derivative AdS gravity theories satisfy the second law.

Abstract

In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary $c$-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in arXiv:1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.