Helical magnetic effect and the chiral anomaly

Abstract

In the presence of the fluid helicity $\mathbf{v}\cdot \mathbf{\omega }$, the magnetic field induces an electric current of the form $\mathbf{j}=C_{\mathrm{HME}}(\mathbf{v}\cdot \mathbf{\omega })\mathbf{B}$. This is the helical magnetic effect (HME). We show that for massless Dirac fermions with charge $e=1$, the transport coefficient $C_{\mathrm{HME}}$ is fixed by the chiral anomaly coefficient $C=1/(2{\pi }^2)$ as $C_{\mathrm{HME}}=C/2$ independently of interactions. We show the conjecture that the coefficient of the magnetovorticity coupling for the local vector charge, $n=C_{B\omega }\mathbf{B}\cdot \mathbf{\omega }$, is related to the chiral anomaly coefficient as $C_{B\omega }=C/2$. We also discuss the condition for the emergence of the helical plasma instability that originates from the HME.

Comments: 13 pages; v2: published version