No Net Charge Separation in Hot QCD in a Magnetic Field

TL;DR

This paper demonstrates that in high-temperature QCD with a magnetic field, the expected charge separation effect does not occur due to the cancellation of two opposing currents, challenging previous claims about the Chiral Magnetic Effect.

Contribution

The study shows that in equilibrium high-temperature QCD, the net charge separation along a magnetic field vanishes, contrasting with earlier predictions of the Chiral Magnetic Effect.

Findings

Electric currents from anomaly and medium effects cancel out

No net charge separation occurs in high-T QCD in a magnetic field

Contrasts with previous claims of the Chiral Magnetic Effect

Abstract

We study the realization of axion electrodynamics in QCD in the presence of a background magnetic field at temperatures high enough for the occurrence of topological charge transitions that are reflected in the presence of a $\theta$-vacuum term in the action. We show that in this system, the Maxwell equations contain two equal and opposite electric currents that are proportional to the time derivative of the axion field $\theta$. One of these currents comes directly from the Abelian chiral anomaly term in the action and can be interpreted as a polarization current due to the magnetoelectricity of the system with CP-broken symmetry. The other current is obtained from the regular tadpole diagrams and can be understood as produced by the medium chiral imbalance and the single spin projection of the quarks in the lowest Landau level. Since the two currents cancel out, the net electric charge separation along the magnetic field, a phenomenon known as the Chiral Magnetic Effect, does not take place in hight-T QCD at least in equilibrium, in sharp contrast with many claims in the literature. We discuss the similarities and differences with Weyl semimetals in a magnetic field.