Gluon spectral functions and transport coefficients in Yang--Mills theory

TL;DR

This paper non-perturbatively computes gluon spectral functions at finite temperature in quenched QCD, derives a relation for the energy-momentum tensor spectral function, and estimates the shear viscosity to entropy ratio across a range of temperatures.

Contribution

It introduces a method to calculate gluon spectral functions and shear viscosity in Yang-Mills theory, providing new quantitative insights into transport properties near the QCD phase transition.

Findings

Shear viscosity to entropy ratio $\,\eta/s$ has a minimum of about 0.115 at 1.25 $T_c$.

Gluon spectral functions are obtained non-perturbatively using maximum entropy method.

The approach links spectral functions to transport coefficients in Yang-Mills theory.

Abstract

We compute non-perturbative gluon spectral functions at finite temperature in quenched QCD with the maximum entropy method. We also provide a closed loop equation for the spectral function of the energy-momentum tensor in terms of the gluon spectral function. This setup is then used for computing the shear viscosity over entropy ratio $\eta/s$ in a temperature range from about $0.4\, T_c$ to $4.5\, T_c$. The ratio $\eta /s$ has a minimum at about $1.25\, T_c$ with the value of about 0.115. We also discuss extensions of the present results to QCD.