Electric-current Susceptibility and the Chiral Magnetic Effect

We compute the electric-current susceptibility \chi of hot quark-gluon matter in an external magnetic field B. The difference between the susceptibilities measured in the directions parallel and perpendicular to the magnetic field is ultraviolet finite and given by \chi^\parallel-\chi^\perp = VTN_c\sum_f q_f^2 |q_f B|/(2\pi^2), where V denotes the volume, T the temperature, N_c the number of colors, and q_f the charge of a quark of flavor f. This non-zero susceptibility difference acts as a background to the Chiral Magnetic Effect, i.e. the generation of electric current along the direction of magnetic field in the presence of topological charge. We propose a description of the Chiral Magnetic Effect that takes into account the fluctuations of electric current quantified by the susceptibility. We find that our results are in agreement with recent lattice QCD calculations. Our approach can be used to model the azimuthal dependence of charge correlations observed in heavy ion collisions.