Does horizon entropy satisfy a Quantum Null Energy Conjecture?

TL;DR

This paper provides evidence that the Hubeny-Rangamani Causal Holographic Information (CHI) satisfies the quantum null energy condition (QNEC) in 1+1 holographic CFTs, supporting its role as a coarse-grained entropy measure in holography.

Contribution

It demonstrates that CHI satisfies the QNEC in specific holographic settings, extending its known properties and supporting its interpretation as a coarse-grained entropy.

Findings

CHI satisfies QNEC in 1+1 holographic CFTs with conical defects in AdS3.

Supports CHI as a meaningful coarse-grained entropy in holography.

Includes derivation of a coarse-grained generalized second law for coupled CFTs and dilaton gravity.

Abstract

A modern version of the idea that the area of event horizons gives $4G$ times an entropy is the Hubeny-Rangamani Causal Holographic Information (CHI) proposal for holographic field theories. Given a region $R$ of a holographic QFTs, CHI computes $A/4G$ on a certain cut of an event horizon in the gravitational dual. The result is naturally interpreted as a coarse-grained entropy for the QFT. CHI is known to be finitely greater than the fine-grained Hubeny-Rangamani-Takayanagi (HRT) entropy when $\partial R$ lies on a Killing horizon of the QFT spacetime, and in this context satisfies other non-trivial properties expected of an entropy. Here we present evidence that it also satisfies the quantum null energy condition (QNEC), which bounds the second derivative of the entropy of a quantum field theory on one side of a non-expanding null surface by the flux of stress-energy across the surface. In particular, we show CHI to satisfy the QNEC in 1+1 holographic CFTs when evaluated in states dual to conical defects in AdS$_3$. This surprising result further supports the idea that CHI defines a useful notion of coarse-grained holographic entropy, and suggests unprecedented bounds on the rate at which bulk horizon generators emerge from a caustic. To supplement our motivation, we include an appendix deriving a corresponding coarse-grained generalized second law for 1+1 holographic CFTs perturbatively coupled to dilaton gravity.