The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory

TL;DR

This paper computes the shear stress correlator in high-temperature Yang-Mills theory at next-to-leading order using ultraviolet expansion, refining a shear sum rule and providing insights into operator product expansions and spectral densities.

Contribution

It provides a next-to-leading order calculation of the shear stress correlator in hot Yang-Mills theory using ultraviolet expansion techniques, refining existing sum rules.

Findings

Refined shear sum rule for Yang-Mills theory.

Operator product expansions for correlators.

Next-to-leading order spectral density results.

Abstract

We determine a next-to-leading order result for the correlator of the shear stress operator in high-temperature Yang-Mills theory. The computation is performed via an ultraviolet expansion, valid in the limit of small distances or large momenta, and the result is used for writing operator product expansions for the Euclidean momentum and coordinate space correlators as well as for the Minkowskian spectral density. In addition, our results enable us to confirm and refine a shear sum rule originally derived by Romatschke, Son and Meyer.