Membrane paradigm, gravitational Θ-term and gauge/gravity duality

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, however, 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 horizon. 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.