Hall viscosity from gauge/gravity duality

TL;DR

This work addresses parity-odd transport in parity-violating (2+1)D fluids by constructing a holographic model with a gravitational θ-term in AdS$_4$. Using the fluid/gravity correspondence and linear response, it derives a membrane-paradigm-type expression for the Hall viscosity, $\eta_A = -\frac{\lambda}{8\pi G_{4}}\frac{r^4 f'(r) \theta'(r)}{4 H^2(r)}\big|_{r_H}$, showing the coefficient is entirely determined by near-horizon data. A Kubo-type formula at zero momentum is proposed and validated against explicit linearized perturbations, strengthening the holographic understanding of Hall viscosity. The results link the Hall response to horizon data and the membrane paradigm, offering a robust holographic handle on parity-odd transport in strongly coupled 2+1D systems.

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.