Suppression of the shear viscosity near the critical temperature in hot QCD

We consider QCD near but above critical temperature T-c. The pressure, susceptibilities and the renormalized Polyakov loop - which is an order parameter for the deconfining phase transition - dramatically change up to temperatures a few times T-c. We refer to this region as a "semi" - QGP, where partial confinement plays important role. We show that the shear viscosity eta is suppressed by two powers of the Polyakov loop. This suggests that eta/T-3 decreases markedly as QCD cools down to temperatures near T-c. We also show a ratio of the viscosity to the entropy becomes small near T-c [1].