We argue that the inferred ratio of shear viscosity to entropy density of the quark-gluon plasma, h/s & 0.5 near the deconfinement temperature Tc, can be understood from perturbative QCD. To rebut opposite views, we first show that the existing leading order result should not be expanded in logarithms. After then settling the question of scale for the running coupling, we establish a temperature dependence of h/s which agrees well with constraints from hydrodynamics.
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