Holographic proof of the averaged null energy condition

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