A holographic proof of the averaged null energy condition

Abstract

The averaged null energy conditions (ANEC) states that, along a complete null curve, the negative energy fluctuations of a quantum field must be balanced by positive energy fluctuations. We use the AdS/CFT correspondence to prove the ANEC for a class of strongly coupled conformal field theories in flat spacetime. A violation of the ANEC in the field theory would lead to acausal propagation of signals in the bulk.

13 pages, 1 figure. v4: corrected an error in the proof, results remain unchanged, v3: added additional references along with minor editorial changes, v2: added additional references and acknowledgments

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• The averaged null energy condition on holographic evaporating black holes
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• Quantum null energy condition in quenched 2d CFTs
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• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows