RG Flow and Thermodynamics of Causal Horizons in AdS

TL;DR

This paper proposes a duality between boundary renormalization group flow and the thermodynamics of causal horizons in AdS, demonstrating that the holographic c-function obeys a second law analogous to thermodynamic entropy increase.

Contribution

It introduces a novel duality linking boundary RG flow to causal horizon thermodynamics and constructs a holographic c-function that satisfies a monotonic second law.

Findings

The boundary RG flow corresponds to dynamical causal horizons in AdS.

The holographic c-function is identified with the Bekenstein-Hawking entropy density.

The c-function monotonically interpolates between UV and IR central charges.

Abstract

Causal horizons in pure Poincare $AdS$ are Killing horizons generated by dilatation vector. Renormalization group (RG) flow breaks the dilatation symmetry and makes the horizons dynamical. We propose that the boundary RG flow is dual to the thermodynamics of the causal horizon. As a check of our proposal we show that the gravity dual of the boundary $c$-theorem is the second law of thermodynamics obeyed by causal horizons. The holographic $c$-function is the Bekenstein-Hawking entropy (density) of the dynamical causal horizon. We explicitly construct the $c$-function in a generic class of RG-flow geometries and show that it interpolates monotonically between the UV and IR central charges as a result of the second law.