Deconfinement in weak electric and magnetic fields

Abstract

We investigate the thermal deconfinement transition in weak electric and magnetic fields, describing the hadronic phase by a pion gas and the quark--gluon plasma by the MIT bag model. Besides the thermal response of each phase, we include the one-loop electromagnetic vacuum terms of quarks and charged pions, renormalized at a common scale that fixes the charge in the confined vacuum. With no fitting of the electromagnetic response, the critical temperature rises with the electric field and falls with the magnetic one. The electric curvature is of the same size as that obtained on the lattice, while the magnetic one is a few times larger. We discuss the dependence on quark mass and renormalization scale, and a large-$N_c$ organization of both curvatures, whose sum is independent of the vacuum terms and connects directly to perturbative QCD.