  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 SYM theory) or asymptotically free (as for the pure Yang-Mills
theory) behavior at large momenta. These sum rules may help constrain QGP
transport coefficients obtained from lattice QCD.
