Finite temperature spectral densities of momentum and R-charge correlators in N=4 Yang-Mills theory

We compute spectral densities of momentum and R-charge correlators in thermal N=4 Yang-Mills theory at strong coupling. For omega similar to T and smaller, the spectral density differs markedly from perturbation theory; there is no kinetic theory peak. For large omega, the spectral density oscillates around the zero temperature result with an exponentially decreasing amplitude. Contrast this with QCD where the spectral density of the current-current correlator approaches the zero temperature result like (T/omega)(4). This difference is related to the absence of cuts in the retarded Green function in N=4 Yang-Mills theory at strong coupling. Despite these marked differences with perturbation theory, in Euclidean space-time the correlators differ by only similar to 10% from the free result. The implications for lattice QCD measurements of transport are discussed.