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The phase diagram and the equation of state of QCD is investigated in thepresence of weak background electric fields by means of continuum extrapolatedlattice simulations. The complex action problem at nonzero electric field iscircumvented by a novel Taylor expansion, enabling the determination of thelinear response of the thermal QCD medium to constant electric fields -- incontrast to simulations at imaginary electric fields, which, as we demonstrate,involve an infrared singularity. Besides the electric susceptibility of QCDmatter, we determine the dependence of the Polyakov loop on the field strengthto leading order. Our results indicate a plasma-type behavior with a negativesusceptibility at all temperatures, as well as an increase in the transitiontemperature as the electric field grows.

QCD phase diagram and equation of state in background electric fields