Abstract
We examine the achronal averaged null energy condition~(ANEC) for a class of conformal field theories~(CFT) at strong coupling in curved spacetime. By applying the AdS/CFT duality, we find holographic models which violate the achronal ANEC for $3+1$ and $4+1$-dimensional boundary theories. In our model, the bulk spacetime is an asymptotically AdS vacuum bubble solution with neither causality violation nor singularities. The conformal boundary of our bubble solution is asymptotically flat and is causally proper in the sense that a "fastest null geodesics" connecting any two points on the boundary must lie entirely on the boundary. We show that conversely, if the spacetime fails to have this causally proper nature, then there must be a naked singularity in the bulk.
Highlights
The classical null energy condition (NEC) Tμνlμlν ≥ 0 for all null vectors l at all points is the key condition for the proof of the singularity theorems, topological censorship theorem, and other important theorems in classical general relativity
We have shown that the achronal averaged null energy condition (ANEC) can be violated in the boundary conformal field theories (CFT) theory with even dimension, due to the conformal anomaly
We have explored possible interplay between the achronal ANEC, the causally proper nature of bulk and boundary spacetimes, and the weak cosmic censorship within the context of AdS=CFT duality
Summary
The classical null energy condition (NEC) Tμνlμlν ≥ 0 for all null vectors l at all points is the key condition for the proof of the singularity theorems, topological censorship theorem, and other important theorems in classical general relativity. It is interesting to study whether the achronal ANEC is violated in a strongly coupled field theory in the framework of the AdS=CFT duality. In this context it was recently shown in [10] that the achronal ANEC holds for a class of conformal field theories in the boundary Minkowski spacetime. Even though the NEC is locally violated near the wormhole throat, the achronal ANEC is kept preserved This suggests that the achronal ANEC may always hold in a thermal state with asymptotically flat boundary spacetime. We further examine the achronal ANEC for a class of strongly coupled field theories in asymptotically flat curved spacetimes in the framework of the AdS=CFT duality.
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