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 eta/s in a temperature range from about 0.4T(c) to 4.5T(c). The ratio eta/s has a minimum at about 1.25T(c) with the value of about 0.115. We also discuss extensions of the present results to QCD.