Hall viscosity from gauge/gravity duality

TL;DR

This paper demonstrates that in a (2+1)-dimensional holographic model with broken parity, the fluid exhibits a nonzero Hall viscosity, which can be computed via fluid/gravity correspondence and confirmed through a Kubo formula.

Contribution

It provides a holographic realization of Hall viscosity in (2+1)-dimensional fluids with broken parity, linking it to near-horizon geometry and deriving a Kubo formula.

Findings

Hall viscosity is nonzero in the holographic model.

Hall viscosity depends only on the near-horizon region.

Kubo formula for Hall viscosity is derived and verified.

Abstract

In (2+1)-dimensional systems with broken parity, there exists yet another transport coefficient, appearing at the same order as the shear viscosity in the hydrodynamic derivative expansion. In condensed matter physics, it is referred to as "Hall viscosity". We consider a simple holographic realization of a (2+1)-dimensional isotropic fluid with broken spatial parity. Using techniques of fluid/gravity correspondence, we uncover that the holographic fluid possesses a nonzero Hall viscosity, whose value only depends on the near-horizon region of the background. We also write down a Kubo's formula for the Hall viscosity. We confirm our results by directly computing the Hall viscosity using the formula.