Finite Temperature Spectral Densities of Momentum and R-Charge Correlators in $\mathbb{N}=4$ Yang Mills Theory

We compute spectral densities of momentum and R-charge correlators in thermal $\mathbb{N}=4$ Yang Mills at strong coupling using the AdS/CFT correspondence. For $\omega \sim T$ 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 $(T\mathrm{/}\omega {)}^4$. Despite these marked differences with perturbation theory, in Euclidean space-time the correlators differ by only $\sim 10$ from the free result. The implications for Lattice QCD measurements of transport are discussed.