Holographic proof of the quantum null energy condition

2015/12/31 by Jason Koeller, Stefan Leichenauer
Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Data mining #Energy condition #Holography #Noncommutative and Quantum Gravity Theories #Null (SQL) #Optics #Physics #Proof of concept #Quantum #Quantum mechanics #Theoretical physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.94.024026

published as Phys. Rev. D 94, 024026 (2016) · 25 pages, 2 figures. v2: references added, minor notation corrections, minor clarifications

arxiv created 2016/05/31 · openalex publication_date 2016/07/12 · arxiv updated 2016/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use holography to prove the quantum null energy condition (QNEC) at leading order in large N for CFTs and relevant deformations of CFTs in Minkowski space which have Einstein gravity duals. Given any codimension-two surface \mathrm\ensuremathΣ which is locally stationary under a null deformation in the direction k at the point p, the QNEC is a lower bound on the energy-momentum tensor at p in terms of the second variation of the entropy to one side of \mathrm\ensuremathΣ: ⟨T_kk⟩\ensuremath≥S^\ensuremath'\ensuremath'/2\ensuremathπ√(h). In a CFT, conformal transformations of this inequality give results which apply when \mathrm\ensuremathΣ is not locally stationary. The QNEC was proven previously for free theories, and taken together with our result this provides strong evidence that the QNEC is a true statement about quantum field theory in general.

Citations

• Area terms in entanglement entropy
• A Positive Mass Theorem Based on the Focusing and Retardation of Null Geodesics
• The Large Scale Structure of Space-Time
• Wormholes, Time Machines, and the Weak Energy Condition
• Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
• Gravitational Collapse and Space-Time Singularities
• Large Mass Hierarchy from a Small Extra Dimension
• The gravity dual of a density matrix
• Holographic c-theorems in arbitrary dimensions
• An Alternative to Compactification
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Black Holes and Entropy
• Averaged energy conditions and quantum inequalities
• Theorems on gravitational time delay and related issues