On chiral magnetic effect and holography

TL;DR

The paper addresses why the chiral magnetic effect (CME) current differs when described by a background axial field versus a finite axial chemical potential, using a holographic AdS/QCD-like model with a Chern-Simons term. It shows that in a static background with constant $A_0^A$ and magnetic field $\mathbf{B}$ the induced current vanishes, while introducing a conserved axial charge with chemical potential $μ_A$ yields the standard anomaly-induced current $\mathbf{j}=\frac{μ_A}{2π^2} e^2 N_c \mathbf{B}$. By defining the conserved charge $Q^5$ and coupling $μ_A$ to it, the paper derives an effective action $S_{eff}=3 κ μ_A \int d^4x \epsilon^{ijk} A_i^V F_{jk}^V$, which reproduces the CME current and aligns holographic results with the triangle anomaly. This work clarifies the necessity of a conserved axial charge for the CME to occur and highlights the roles of gauge invariance and anomaly structure in holographic models.

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 ${\bf j} = \frac{μ_A}{2π^2}e^2 N_c {\bf B}$.