Physical Effects of the Gravitational Θ-Parameter

We describe the effect of the gravitational Θ-parameter on the behavior of the stretched horizon of a black hole in (3+1)-dimensions. The gravitational Θ-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 Θ-term induces a non-trivial contact term in the energy-momentum 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 Θ-term acquires the same third order parity violating transport coefficient.