Holographic Proof of the Quantum Null Energy Condition

Dec 18, 2015
14 pages
Published in:
  • Phys.Rev.D 94 (2016) 2, 024026
  • Published: Jul 12, 2016
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Abstract: (APS)
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 Σ 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 Σ: ⟨Tkk⟩≥S′′/2πh. In a CFT, conformal transformations of this inequality give results which apply when Σ 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.
Note:
  • 25 pages, 2 figures. v2: references added, minor notation corrections, minor clarifications
  • transformation: conformal
  • gravitation: duality
  • space: Minkowski
  • null-energy condition
  • deformation
  • field theory
  • holography
  • expansion 1/N
  • higher-order: 0