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

We compute the electric conductivity of quark matter at finite temperature T and a quark chemical potential mu under a magnetic field B beyond the lowest Landau level approximation. The electric conductivity transverse to B is dominated by the Hall conductivity sigma(H). For the longitudinal conductivity sigma vertical bar vertical bar, we need to solve kinetic equations. Then, we numerically find that sigma vertical bar vertical bar has only a mild dependence on mu and the quark mass m(q). Moreover, sigma vertical bar vertical bar 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 sigma vertical bar vertical bar at a nonzero B remains within the range of the lattice-QCD estimate at B = 0.