Physical effects of the gravitational Θ-parameter

We describe the effect of the gravitational Theta-parameter on the behavior of the stretched horizon of a black hole in (3+ 1)-dimensions. The gravitational Theta-term is a total derivative, however, it 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. In the context of the gauge/gravity duality, the Theta-term induces a nontrivial contact term in the energymomentum tensor of a (2 + 1)-dimensional large-N gauge theory, which admits a dual gravity description. As a consequence, the dual gauge theory in the presence of the Theta-term acquires the same third-order parity violating transport coefficient.