On electric fields in hot QCD: infrared regularization dependence

We study the impact of background electric fields on a hot plasma of charged particles -- a setting relevant for the early stages of heavy-ion collisions as well as laser pulse experiments. Historically, the electric susceptibility -- encoding the behavior of the hot medium for weak fields -- has been defined within two different formalisms, leading to two distinct results at nonzero temperature. With the help of an exact fermion propagator in a homogeneous electric background field at nonzero temperature and finite volume on the one hand, and an improved perturbative result on the other, we identify the origin of this disagreement. The equilibrium conditions for the system are discussed and the role of the thermodynamic ensemble used to describe the system is highlighted. Finally, we construct the electric susceptibility in a simplified hadron resonance gas model, relevant for the strongly interacting medium in the low-temperature regime.