The Quantum Null Energy Condition, Entanglement Wedge Nesting, and Quantum Focusing

Abstract

We study the consequences of Entanglement Wedge Nesting for CFTs with holographic duals. The CFT is formulated on an arbitrary curved background, and we include the effects of curvature-squared couplings in the bulk. In this setup we find necessary and sufficient conditions for Entanglement Wedge Nesting to imply the Quantum Null Energy Condition in $d\le 5$, extending its earlier holographic proofs. We also show that the Quantum Focusing Conjecture yields the Quantum Null Energy Condition as its nongravitational limit under these same conditions.

20+12 pages, 1 figure

References in corpus (8)

• Entanglement Entropy, Trace Anomalies and Holography
• Markov property of the CFT vacuum and the a-theorem
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• New Exact Solutions of Quadratic Curvature Gravity
• Geometric Constraints from Subregion Duality Beyond the Classical Regime
• The Quantum Null Energy Condition in Curved Space
• Violating the Quantum Focusing Conjecture and Quantum Covariant Entropy Bound in $d\ge 5$ dimensions
• The Quantum Focusing Conjecture Has Not Been Violated

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• Surface Theory: the Classical, the Quantum, and the Holographic
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• The Quantum Entropy Cone of Hypergraphs
• Seeing the Entanglement Wedge
• Geometrical tools for embedding fields, submanifolds, and foliations
• Bare Quantum Null Energy Condition
• Holographic entanglement entropy is cutoff-covariant
• A framework for generalizing toric inequalities for holographic entanglement entropy
• How Much NEC Breaking Can the Universe Endure?
• Disentanglement as a strong cosmic censor
• QNEC-Preserving IR Regulators for the Entropy
• Constraints from Entanglement Wedge Nesting for Holography at a Finite Cutoff