The chiral magnetic effect in hydrodynamical approach

We consider a model with two conserved currents, vector and axial, and two associated chemical potentials, μ and μ5. In the presence of external magnetic and electric fields the axial current is anomalous. Generalizing recent results and using thermodynamic relations alone we demonstrate that one can evaluate the chiral magnetic effect (ChME), that is the electric current flowing in the direction of the external magnetic field. In the linear in the chemical potential approximation the current is the same as for non-interacting fermions. In other words, there exists a hydrodynamic “non-renormalization theorem for the ChME”.