On electric fields in hot QCD: perturbation theory

We investigate the response of a hot gas of quarks to external electric fields via leading-order perturbation theory. In particular, we discuss how equilibrium is maintained in the presence of the electric field and calculate the electric susceptibility, providing its high-temperature expansion for arbitrary quark mass. Furthermore, we point out that there is a mismatch between this, direct determination of the susceptibility at zero field and the weak-field expansion of the effective action at nonzero electric fields, as obtained using Schwinger’s exact propagator. We discuss the origin of this mismatch and elaborate on the generalization of our results to full QCD in electric fields.