Electric Conductivity of Hot and Dense Quark Matter in a Magnetic Field with Landau Level Resummation via Kinetic Equations

Abstract

We compute the electric conductivity of quark matter at finite temperature T and a quark chemical potential μ under a magnetic field B beyond the lowest Landau level approximation. The electric conductivity transverse to B is dominated by the Hall conductivity σH. For the longitudinal conductivity σ we need to solve kinetic equations. Then, we numerically find that σ has only a mild dependence on μ and the quark mass mq. Moreover, σ first decreases and then linearly increases as a function of B, leading to an intermediate B region that looks consistent with the experimental signature for the chiral magnetic effect. We also point out that σ at a nonzero B remains within the range of the lattice-QCD estimate at B=0.