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.

Figures (1)

• Figure 1: (a) Two curves which begin and end on the conformal boundary but which dip into the bulk. The assumption of good causality requires that the curve which ends outside of the boundary light cone (dashed line) cannot be causal. (b) Schematic of the construction used in our proof. The solid line is the conformal boundary $z=0$ and the dashed lines represent causal curves extending into the bulk. The $v$ direction has been suppressed in this diagram.