Chiral Magnetic Effect in Hydrodynamic Approximation

TL;DR

This paper reviews the derivation of the chiral magnetic effect within hydrodynamics, emphasizing its non-renormalization and connection to quantum anomalies, and discusses the implications for dissipationless current and potential microscopic mechanisms.

Contribution

It demonstrates that the chiral magnetic effect remains unchanged in hydrodynamics despite strong interactions, using thermodynamics and anomaly theorems, and discusses its quantum and microscopic aspects.

Findings

ChME is not renormalized in hydrodynamics.

The effect is a dissipation-free, ballistic transport phenomenon.

ChME remains unmodified in superfluid conditions.

Abstract

We review derivations of the chiral magnetic effect (ChME) in hydrodynamic approximation. The reader is assumed to be familiar with the basics of the effect. The main challenge now is to account for the strong interactions between the constituents of the fluid. The main result is that the ChME is not renormalized: in the hydrodynamic approximation it remains the same as for non-interacting chiral fermions moving in an external magnetic field. The key ingredients in the proof are general laws of thermodynamics and the Adler-Bardeen theorem for the chiral anomaly in external electromagnetic fields. The chiral magnetic effect in hydrodynamics represents a macroscopic manifestation of a quantum phenomenon (chiral anomaly). Moreover, one can argue that the current induced by the magnetic field is dissipation free and talk about a kind of "chiral superconductivity". More precise description is a ballistic transport along magnetic field taking place in equilibrium and in absence of a driving force. The basic limitation is exact chiral limit while the temperature--excitingly enough- does not seemingly matter. What is still lacking, is a detailed quantum microscopic picture for the ChME in hydrodynamics. Probably, the chiral currents propagate through lower-dimensional defects, like vortices in superfluid. In case of superfluid, the prediction for the chiral magnetic effect remains unmodified although the emerging dynamical picture differs from the standard one.