Chiral magnetic response to arbitrary axial imbalance

TL;DR

This paper analyzes how chiral fermions respond to arbitrary axial imbalances in the presence of magnetic fields, revealing the importance of local charge conservation, regularization effects, and the conditions under which the chiral magnetic effect manifests.

Contribution

It provides an analytical expression for the chiral magnetic conductivity under arbitrary axial imbalance and discusses the impact of inhomogeneities and regularization on the CME.

Findings

CME current vanishes for spatially oscillating axial charge.

Homogeneous axial imbalance yields CME current determined by the anomaly.

Regularization affects the limit of constant axial imbalance.

Abstract

The response of chiral fermions to time and space dependent axial imbalance & constant magnetic field is analyzed. The axialvector-vector-vector (AVV) three-point function is studied using a real-time approach at finite temperature in the weak external field approximation. The chiral magnetic conductivity is given analytically for noninteracting fermions. It is pointed out that local charge conservation plays an important role when the axial imbalance is inhomogeneous. Proper regularization is needed which makes the constant axial imbalance limit delicate: for static but spatially oscillating chiral charge the current of the chiral magnetic effect (CME) vanishes. In the homogeneous (but possible time-dependent) limit of the axial imbalance the CME current is determined solely by the chiral anomaly. As a phenomenological consequence, the observability of the charge asymmetry caused by the CME turns out to be a matter of interplay between various scales of the system. Possible plasma instabilities resulting from the gradient corrections to the CME current are also pointed out.