On magnetostatics of chiral media

Abstract

We consider magnetostatics of chiral media with a non-vanishing chiral chemical potential μ5≠0. In such media, the chiral anomaly has macroscopic manifestations which go beyond the standard classical electrodynamics. A new term in the effective action takes form of a topological three-dimensional photon mass. The topological mass turns to be imaginary and signals instability. Namely, magnetic field with non-trivial helicity is generated spontaneously. A stable state corresponds to a solution of the Beltrami equations. From the action relevant to instability, we show also that the interaction between two current loops reduces to the linking number of the loops. In addition, we observe the vanishing of the chiral magnetic conductivity in the strict static and uniform limit.