The Chiral Magnetic Effect and Axial Anomalies

Understand

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.