Electrical conductivity of strongly magnetized relativistic plasma

We employ first-principles quantum field theoretical methods to investigate the longitudinal and transverse electrical conductivities of a strongly magnetized hot relativistic plasma at the leading order in coupling. The conductivities exhibit an approximate scaling behavior expressed in terms of dimensionless functions of eB/T^2, where T represents the temperature and B the magnetic field. We demonstrate that the underlying mechanisms governing the transverse and longitudinal conductivities differ significantly, resulting in substantial suppression of the former compared to the latter. We formally extend our analysis to a magnetized quark-gluon plasma, although the approximation may be unreliable at strong coupling.