Physical Effects of the Gravitational $\Theta$-Parameter

TL;DR

This paper investigates how the gravitational $ heta$-parameter influences black hole horizon dynamics and dual gauge theory transport properties, revealing a new third order parity-violating transport coefficient.

Contribution

It demonstrates that the gravitational $ heta$-term induces a novel third order parity-violating transport coefficient on black hole horizons and in dual gauge theories.

Findings

The $ heta$-term affects horizon scrambling behavior.

A new third order parity-violating transport coefficient is identified.

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

Abstract

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 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 $\Theta$-term acquires the same third order parity violating transport coefficient.