Photon and dilepton production in the Quark-Gluon plasma: perturbation theory vs lattice QCD

This talk reviews the status of QCD calculations of photon and dilepton production rates in a Quark-Gluon plasma. Theses rates are known to order ${\cal O}(\alpha_s)$. Their calculations involve various resummations to account for well identified physical effects that are briefly described. Lattice calculations of the spectral functions give also access to the dilepton rates. Comparison with perturbative results points to inconsistencies in both approaches when the dilepton energy becomes small.