Classical effective theory for hot QCD

In high temperature QCD, the perturbation theory is plagued with infrared divergences which reflect long-range non-perturbative phenomena. I argue that it is possible to study such phenomena within a classical thermal field theory which can be put on a three-dimensional lattice. The classical theory is an effective theory for the soft, non-perturbative modes, as obtained after integrating out the hard modes in perturbation theory. It is well suited for numerical studies of the non-perturbative real-time dynamics, which cannot be studied within the standard, imaginary-time formulations of lattice QCD.