On Magnetostatics of Chiral Media

We consider magnetostatics of chiral media with a non-vanishing chiral chemical potential $μ_5\neq 0$. The chiral anomaly is known to have macroscopic manifestations which go beyond the standard classical electrodynamics and we introduce an effective action which accounts for the effect of the anomaly. A new piece in the effective action takes the form of a topological three-dimensional photon mass. The topological mass of the photon turns to be imaginary and signals instability. A stable state corresponds to a solution of the Beltrami equations. We demonstrate also that the interaction between two current loops reduces to the linking number of the loops. As for the chiral magnetic effect it seems to disappear in the far infrared.

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