Transport Coefficients in Yang--Mills Theory and QCD

TL;DR

This paper calculates the shear viscosity to entropy density ratio in Yang--Mills theory using spectral functions and provides an analytic fit for its temperature dependence, extending insights towards QCD.

Contribution

It introduces an exact diagrammatic approach to compute $ta/s$ in Yang--Mills theory and offers the first estimate of this ratio in QCD.

Findings

Analytic fit formula for $ta/s$ across temperature range.

Consistent high-temperature behavior with perturbative results.

First estimate of $ta/s$ in QCD.

Abstract

We calculate the shear viscosity over entropy density ratio $\eta/s$ in Yang--Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of $\eta/s$ over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for $\eta/s$ in QCD.