Lattice gauge theory sum rule for the shear channel

An exact expression is derived for the (omega, p) = 0 thermal correlator of shear stress in SU(N-c) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when omega -> infinity. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as alpha(2)(s)(omega) and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for T greater than or similar to 3T(c). By contrast with the bulk channel, the shear channel spectral density is then overall enhanced as compared to the spectral density in vacuo.