Abstract
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 $\ensuremath{\eta}/s$ in a temperature range from about $0.4{T}_{c}$ to $4.5{T}_{c}$. The ratio $\ensuremath{\eta}/s$ 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.
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