Suppression of the shear viscosity in a ``semi''-quark-gluon plasma

We consider QCD at temperatures T near T_c, where the theory deconfines. We distinguish between a “complete” quark-gluon plasma (QGP), where the vacuum expectation value of the renormalized Polyakov loop is near unity, essentially constant with T, and the “semi”-QGP, where the loop changes strongly with T. Lattice simulations indicate that in QCD, there is a semi-QGP from below T_c to a few times that. Using a semiclassical model, we compute the shear viscosity, η, to leading order in perturbation theory. We find that near T_c, where the expectation value of the Polyakov loop is small, that η/T³ is suppressed by two powers of the loop. For heavy ions, this suggests that during the initial stages of the collision, hydrodynamic behavior at the LHC will be characterized by a shear viscosity which is significantly larger than that at RHIC.