Spectral sum rules for the quark-gluon plasma

We derive sum rules involving the spectral density of the stress-energy tensor in N=4 super-Yang-Mills theory and pure Yang-Mills theory. The sum rules come from the hydrodynamic behavior at small momenta and the conformal (in the case of N=4 super-Yang-Mills theory) or asymptotically free (as for the pure Yang-Mills theory) behavior at large momenta. These sum rules may help constrain quark-gluon plasma transport coefficients obtained from lattice QCD.