The chiral magnetic effect in hydrodynamical approach

TL;DR

The paper investigates the chiral magnetic effect within a hydrodynamic framework that includes vector and axial currents and the chiral anomaly. Using a two-current model and an entropy-current construction augmented by terms $D \omega^{\mu}$ and $D_B B^{\mu}$, the authors derive constraints from the second law and obtain the leading ChME coefficient. They find $\Delta j^{\mu} = \frac{e^2 \mu_5}{2\pi^2} B^{\mu}$ (with a color generalization to $N_c$ colors), matching the non-interacting result in the linear $\mu_5$ regime, while higher-order dependence on chemical potentials is not fixed thermodynamically. This work suggests a non-renormalization-like property for the ChME coefficient in the linear regime and demonstrates that hydrodynamics can capture anomaly-induced transport in the infrared.

Abstract

In quark-gluon plasma nonzero chirality can be induced by the chiral anomaly. When a magnetic field is applied to a system with nonzero chirality an electromagnetic current is induced along the magnetic field. This phenomenon is called the chiral magnetic effect. In this paper appearance of the chiral magnetic effect in hydrodynamical approximation is shown. We consider a hydrodynamical model for chiral liquid with two independent currents of left and right handed particles in the presence of the chiral anomaly.