Violation of the quantum null-energy condition in a holographic wormhole and infrared effects
Akihiro Ishibashi (Department of Physics and Research Institute for Science and Technology, Kindai University, Higashi-Osaka 577-8502, Japan); Kengo Maeda (Faculty of Engineering, Shibaura Institute of Technology, Saitama 330-8570, Japan); Eric Mefford (Department of Physics, University of California, Santa Barbara, California 93106, USA, Centre de Physique Théorique, École Polytechnique, CNRS, F-91128 Palaiseau, France)
We examine the quantum null energy condition (QNEC) for a -dimensional conformal field theory (CFT) at strong coupling in the background of a wormhole spacetime by employing the correspondence. First, we numerically construct a novel -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.
