On Magnetostatics of Chiral Media

TL;DR

This paper explores the magnetostatics of chiral media with non-zero chiral chemical potential, revealing a topological photon mass, instability conditions, and the behavior of the chiral magnetic effect in the infrared.

Contribution

It introduces an effective action incorporating the chiral anomaly, including a topological photon mass, and analyzes stability and topological interactions in chiral media.

Findings

Topological photon mass is imaginary, indicating instability.

Stable states satisfy Beltrami equations.

Interaction between current loops relates to linking number.

Abstract

We consider magnetostatics of chiral media with a non-vanishing chiral chemical potential $\mu_5\neq 0$. 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.