Geometric Constraints from Subregion Duality Beyond the Classical Regime

TL;DR

This paper explores geometric constraints in AdS/CFT subregion duality beyond the classical limit, connecting various energy and causality conditions to ensure consistency of holographic principles at all orders.

Contribution

It establishes the logical links between key geometric and energy conditions in holography without relying on classical approximations, extending validity beyond the classical regime.

Findings

Constraints hold to all orders in $G\hbar$, not just classical limit.

Provides nontrivial consistency checks for subregion duality.

Connects entanglement wedge properties with energy and causality conditions.

Abstract

Subregion duality in AdS/CFT implies certain constraints on the geometry: entanglement wedges must contain causal wedges, and nested boundary regions must have nested entanglement wedges. We elucidate the logical connections between these statements and the Quantum Focussing Conjecture, Quantum Null Energy Condition, Boundary Causality Condition, and Averaged Null Energy Condition. Our analysis does not rely on the classical limit of bulk physics, but instead works to all orders in $G\hbar \sim 1/N$. This constitutes a nontrivial check on the consistency of subregion duality, entanglement wedge reconstruction, and holographic entanglement entropy beyond the classical regime.