The Chiral Magnetic Effect and Axial Anomalies

TL;DR

This paper provides an elementary derivation of the chiral magnetic effect using magnetic field projections and axial anomalies, linking it to phenomena like the chiral magnetic spiral and mode distortions in QCD and QED.

Contribution

It introduces a novel derivation of the chiral magnetic effect based on Landau-level projection and axial anomalies, connecting it to the Peierls instability and mode distortions.

Findings

Derivation of the chiral magnetic effect from Landau-level projection and axial anomalies.

Identification of the chiral magnetic spiral as a consequence of the effect.

Analysis of mode distortions due to spin and chirality projections in QCD and QED.

Abstract

We give an elementary derivation of the chiral magnetic effect based on a strong magnetic field lowest-Landau-level projection in conjunction with the well-known axial anomalies in two- and four-dimensional space-time. The argument is general, based on a Schur decomposition of the Dirac operator. In the dimensionally reduced theory, the chiral magnetic effect is directly related to the relativistic form of the Peierls instability, leading to a spiral form of the condensate, the chiral magnetic spiral. We then discuss the competition between spin projection, due to a strong magnetic field, and chirality projection, due to an instanton, for light fermions in QCD and QED. The resulting asymmetric distortion of the zero modes and near-zero modes is another aspect of the chiral magnetic effect.