Lattice Gauge Theory Sum Rule for the Shear Channel

Understand

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.