Gluon spectral functions and transport coefficients in Yang-Mills theory

We compute nonperturbative 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 η/s in a temperature range from about 0.4Tc to 4.5Tc. The ratio η/s has a minimum at about 1.25Tc with the value of about 0.115. We also discuss extensions of the present results to QCD.