Helical magnetic effect and the chiral anomaly

Abstract

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