Helicity conservation in perfect electromagnetic and chiral fluids

TL;DR

This paper derives and analyzes helicity conservation laws in perfect electromagnetic and chiral fluids, revealing their connections to chiral anomalies and exploring effects of chiral imbalance in relativistic and non-relativistic regimes.

Contribution

It introduces a unified helicity conservation framework for electromagnetic and chiral fluids, linking it to chiral anomalies and extending to non-relativistic limits.

Findings

Helicity conservation law matches chiral anomaly form in isentropic fluids.

Non-relativistic limit agrees with Abanov-Wiegmann equation at zero temperature.

Chiral imbalance modifies the helicity conservation law significantly.

Abstract

We derive the total helicity conservation law for a perfect electromagnetic relativistic fluid. As the conservation equation contains the derivative of the magnetic helicity, it can be reshaped as having the same form as the chiral anomaly equation if the fluid is isentropic. We also take the non-relativistic limit of the helicity conservation law, and check the agreement with the Abanov-Wiegmann equation at zero temperature, but we provide further corrections in the more general case. We then consider chiral fluids, when the chiral anomaly equation has to be incorporated in the hydrodynamical equations, together with other chiral transport effects which exist in the presence of a chiral imbalance. We finally study how the chiral imbalance modifies the helicity conservation law.