Lattice Gauge Theory Sum Rule for the Shear Channel

TL;DR

This paper derives an exact sum rule for the shear stress correlator in SU(N_c) lattice gauge theory, showing how to handle divergences and analyzing the spectral function's behavior at high frequencies, with implications for understanding thermal properties.

Contribution

It introduces a new linear combination of correlators to remove divergences and establishes a sum rule for the shear spectral function in lattice gauge theory.

Findings

The shear spectral function vanishes at high frequencies at least as fast as α_s^2(ω).

A sum rule for the shear correlator is derived and validated.

The trace anomaly's contribution is estimated to be small for T ≥ 3T_c.

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.