On consistency of hydrodynamic approximation for chiral media

TL;DR

This paper investigates the behavior of chiral liquids with massless fermions, focusing on their electromagnetic currents, potential instabilities, and the validity of hydrodynamic approximations in describing their dynamics.

Contribution

It analyzes the stability and infrared properties of chiral liquids, highlighting conditions under which instabilities and vortex formations occur, and discusses the consistency of hydrodynamic models for such media.

Findings

Instabilities can occur even as electromagnetic coupling approaches zero.

Chiral chemical potential can lead to decay into vortex-containing states.

Hydrodynamic approximation may have limitations in describing chiral media.

Abstract

We consider chiral liquids, that is liquids consisting of massless fermions and right-left asymmetric. In such media, one expects existence of electromagnetic current flowing along an external magnetic field, associated with the chiral anomaly. The current is predicted to be dissipation-free. We consider dynamics of chiral liquids, concentrating on the issues of possible instabilities and infrared sensitivity. Instabilities arise, generally speaking, already in the limit of vanishing electromagnetic constant, $\alpha_{el}\to 0$. In particular, liquids with non-vanishing chiral chemical potential might decay into right-left asymmetric states containing vortices.