Dileptons, spectral weights, and conductivity in the Quark-Gluon Plasma

We re-examine soft dilepton emission from a weakly coupled Quark-Gluon Plasma. We show that Braaten, Pisarski, and Yuan's result that the dilepton rate rises as E^-4 (and the spectral weight scales as 1/E) at small energy E<<gT is correct, but that the coefficient they found for this behavior is not correct, because their analysis was incomplete. At still smaller scales, the behavior moderates to ~1/E^2 for E <= g^4 T, consistent with a finite electrical conductivity. We evaluate the spectral weight in the E~g^4 T region by kinetic theory techniques and show that it satisfies a sum rule, which makes the determination of electrical conductivity from the Euclidean correlation function very challenging.