Does horizon entropy satisfy a Quantum Null Energy Conjecture?

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.

29 pages, 5 figures; v2: minor corrections; v3: 30 pages, 6 figures, modifications to address referee comments, one figure added

References in corpus (5)

• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Entwinement and the emergence of spacetime
• Renormalized entanglement entropy
• The Physical Process First Law for Bifurcate Killing Horizons
• State-Dependent Divergences in the Entanglement Entropy

Cited by in corpus (7)

• Quantum Null Energy Condition and its (non)saturation in 2d CFTs
• A Lower Bound on the Energy Density in Classical and Quantum Field Theories
• Local quantum energy conditions in non-Lorentz-invariant quantum field theories
• Geometric Constraints from Subregion Duality Beyond the Classical Regime
• Essential core of the Hawking--Ellis types
• Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification
• Causal holographic information does not satisfy the linearized quantum focusing condition