Electrical conductivity of quark-gluon plasma in strong magnetic fields

We compute the electrical conductivity of quark-gluon plasma in a strong magnetic field B with quantum field theory at finite temperature using the lowest Landau level approximation. We provide the one-loop result arising from 1-to-2 scattering processes of which the kinematics are satisfied by the ($1+1$)-dimensional fermion dispersion relation. Because of the chirality conservation, the conductivity diverges in the massless limit and is sensitive to the value of the current quark mass. As a result, we find that the conductivity along the direction of the magnetic field is quite large compared with the value at $B=0$, mainly because of the small value of the current quark mass. We show that the resummation of the ladder diagrams for the current-current correlator gives rise to only subleading contributions beyond the leading-log order and thus verify our one-loop result at the leading-log accuracy. We also discuss possible implications for the relativistic heavy-ion collisions.