  The phase diagram and the equation of state of QCD is investigated in the
presence of weak background electric fields by means of continuum extrapolated
lattice simulations. The complex action problem at nonzero electric field is
circumvented by a novel Taylor expansion, enabling the determination of the
linear response of the thermal QCD medium to constant electric fields -- in
contrast to simulations at imaginary electric fields, which, as we demonstrate,
involve an infrared singularity. Besides the electric susceptibility of QCD
matter, we determine the dependence of the Polyakov loop on the field strength
to leading order. Our results indicate a plasma-type behavior with a negative
susceptibility at all temperatures, as well as an increase in the transition
temperature as the electric field grows.
