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

Understand

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 $d\leq 5$, 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.