Membrane Paradigm, Gravitational Θ-Term and Gauge/Gravity Duality
UTTG-21-15 TCC-010-15 Membrane Paradigm, Gravitational Θ-Term and Gauge/Gravity Duality Willy Fischlera;b, Sandipan Kunduc aTheory Group, Department of Physics, University of Texas, Austin, TX 78712, USA bTexas Cosmology Center, University of Texas, Austin, TX 78712, USA cDepartment of Physics, Cornell University, Ithaca, New York, 14853, USA E-mail: fischler@physics.utexas.edu, kundu@cornell.edu Abstract: Following the membrane paradigm, we explore the effect of the gravitational Θ-term on the behavior of the stretched horizon of a black hole in (3 + 1)-dimensions. We reformulate the membrane paradigm from a quantum path-integral point of view where we interpret the macroscopic properties of the horizon as effects of integrating out the region inside the horizon. The gravitational Θ-term is a total derivative, how- ever, using our framework we show that this term affects the transport properties of the horizon. In particular, the horizon acquires a third order parity violating, dimensionless transport coefficient which affects the way localized perturbations scramble on the hori- zon. Then we consider a large-N gauge theory in (2 + 1)−dimensions which is dual to an asymptotically AdS background in (3 + 1)−dimensional spacetime to show that the Θ-term induces a non-trivial contact term in the energy-momentum tensor of the dual theory. As a consequence, the dual gauge theory in the presence of the Θ-term acquires the same third order parity violating transport coefficient. arXiv:1512.01238v2 [hep-th] 13 May 2016 Contents 1 Introduction1 2 Integrating
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