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

We consider QCD near but above critical temperature Tc. 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 Tc. 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 Tc. We also show a ratio of the viscosity to the entropy becomes small near Tc.