On chiral magnetic effect and holography

TL;DR

This paper clarifies the differences in the behavior of fermionic systems and their holographic models under background axial fields versus finite chiral chemical potential, especially regarding the induced electric current.

Contribution

It highlights a key distinction in the chiral magnetic effect between systems with background axial fields and those with finite chiral chemical potential, refining theoretical understanding.

Findings

Electric current vanishes with background axial field $A_0$ and magnetic field.

Electric current follows the anomaly formula with finite chiral chemical potential.

Clarifies the conditions under which the chiral magnetic effect occurs.

Abstract

We point out that there is a difference between the behavior of fermionic systems (and their holographic analogs) in a background axial vector field, on the one hand, and at finite chiral chemical potential, on the other. In the former case, the electric current induced by constant background axial field $A_0$ and magnetic field ${\bf B}$ vanishes, while in the latter it is given by the anomaly-prescribed formula ${\bf j} = \frac{\mu_A}{2\pi^2}e^2 N_c {\bf B}$.