We examine the quantum null energy condition (QNEC) for a $2+1$-dimensional conformal field theory (CFT) at strong coupling in the background of a wormhole spacetime by employing the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. First, we numerically construct a novel $3+1$-dimensional vacuum AdS black hole solution with nontrivial topology, which is dual to a wormhole geometry connecting two flat universes. Although the bulk null energy condition (NEC) is not violated, the NEC for the holographic stress-energy tensor is violated near the wormhole throat. Next, we investigate the entanglement entropy for a half-space anchored to the boundary wormhole throat. We propose a natural prescription for regularizing the IR divergent part of the entanglement entropy and show that the QNEC is violated at the throat. This is the first counterexample to the QNEC, indicating that IR effects are crucial.

• Received 28 August 2018
• Corrected 24 January 2019

DOI:https://doi.org/10.1103/PhysRevD.99.026004

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Published by the American Physical Society