Thermal dilepton rates and electrical conductivity of the QGP from the lattice

We investigate the temperature dependence of the thermal dilepton rate and the electrical conductivity of the gluon plasma at temperatures of 1.1, 1.3, and 1.5Tc in quenched QCD. Making use of nonperturbatively clover-improved Wilson valence quarks allows for a clean extrapolation of the vector meson correlation function to the continuum limit. We found that the vector correlation function divided by T³ is almost temperature independent in the current temperature window. The spectral functions are obtained by χ² fitting of phenomenologically inspired Ans\"atze for the spectral function to the continuum extrapolated correlator data, where the correlations between the data points have been included. Systematic uncertainties arising from varying the Ans\"atze motivated from strong coupling theory as well as perturbation theory are discussed and estimated. We found that the electrical conductivity of the hot medium, related to the slope of the vector spectral function at zero frequency and momentum, is 0.2Cₑₘσ/T0.7Cₑₘ for T=1.1Tc and 0.2Cₑₘσ/T0.4Cₑₘ for the higher temperatures. The dilepton rates and soft photon rates, resulting from the obtained spectral functions, show no significant temperature dependence, either.