Parity-Violating Hydrodynamics in 2+1 Dimensions

TL;DR

This paper classifies and constrains parity-violating transport coefficients in 2+1 dimensional relativistic hydrodynamics, revealing their dissipationless nature and providing a holographic example for their computation.

Contribution

It provides a comprehensive classification of first-order parity-violating transport coefficients and derives constraints from response functions and entropy production positivity.

Findings

All parity-violating coefficients are dissipationless.

Some coefficients relate to magnetic field response and vorticity.

A holographic model computes these coefficients explicitly.

Abstract

We study relativistic hydrodynamics of normal fluids in two spatial dimensions. When the microscopic theory breaks parity, extra transport coefficients appear in the hydrodynamic regime, including the Hall viscosity, and the anomalous Hall conductivity. In this work we classify all the transport coefficients in first order hydrodynamics. We then use properties of response functions and the positivity of entropy production to restrict the possible coefficients in the constitutive relations. All the parity-breaking transport coefficients are dissipationless, and some of them are related to the thermodynamic response to an external magnetic field and to vorticity. In addition, we give a holographic example of a strongly interacting relativistic fluid where the parity-violating transport coefficients are computable.