Lattice Gauge Theory Sum Rule for the Shear Channel

Abstract

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 $\omega \to \infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as ${\alpha }_s^2(\omega )$ 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 $T\gtrsim 3T_c$. By contrast with the bulk channel, the shear channel spectral density is then overall enhanced as compared to the spectral density in vacuo.

11 pages, no figures

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