The chiral magnetic effect and axial anomalies

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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. © Springer-Verlag Berlin Heidelberg 2013.

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Başar, G., & Dunne, G. V. (2013). The chiral magnetic effect and axial anomalies. Lecture Notes in Physics, 871, 261–294. https://doi.org/10.1007/978-3-642-37305-3_10

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