Membrane Paradigm, Gravitational $\Theta$-Term and Gauge/Gravity Duality

TL;DR

This paper investigates how the gravitational $ heta$-term influences black hole horizon properties and dual gauge theories, revealing a new parity-violating transport coefficient affecting perturbation scrambling and energy-momentum contact terms.

Contribution

It reformulates the membrane paradigm to include the gravitational $ heta$-term and demonstrates its effect on horizon transport properties and dual gauge theory contact terms.

Findings

The $ heta$-term induces a third order parity-violating transport coefficient.

The horizon's scrambling behavior is affected by the $ heta$-term.

The dual gauge theory acquires a corresponding contact term in the energy-momentum tensor.

Abstract

Following the membrane paradigm, we explore the effect of the gravitational $\Theta$-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 $\Theta$-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 $\Theta$-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 $\Theta$-term acquires the same third order parity violating transport coefficient.