Energy-momentum tensor correlators and spectral functions

TL;DR

This paper computes energy-momentum tensor correlators and spectral functions in pure gauge theories at finite temperature, aiming to enhance the extraction of transport coefficients like viscosities from lattice QCD data.

Contribution

It provides leading-order perturbative calculations of Euclidean correlators and spectral functions, highlighting methods to improve viscosity extraction from lattice simulations.

Findings

Spectral functions free of large ultraviolet background terms.

Shear and bulk viscosities can be extracted from correlators at small non-zero momentum.

Results aid in interpreting lattice QCD data for transport properties.

Abstract

We calculate the thermal Euclidean correlators and the spectral functions of the energy-momentum tensor for pure gauge theories, including at non-zero spatial momentum, at leading order in perturbation theory. Our goal is to improve the extraction of transport properties from Euclidean correlators that are computable in lattice QCD. Based on our results and the predictions of hydrodynamics for the structure of the spectral functions at low frequencies, we show that the shear and bulk viscosities can advantageously be extracted from the Euclidean correlators of the conserved charges, energy and momentum, at small but non-vanishing spatial momentum. The spectral functions in these channels are free of the ultraviolet $\omega^4$ term which represents a large background to the thermal physics encoded in the correlators of the fluxes.