Shear viscosity in a gluon gas

The relation of the shear viscosity coefficient to the recently introduced transport rate is derived within relativistic kinetic theory. We calculate the shear viscosity over entropy ratio eta/s for a gluon gas, which involves elastic gg -> gg perturbative QCD (PQCD) scatterings as well as inelastic gg <-> ggg PQCD bremsstrahlung. For alpha(s)=0.3 we find eta/s=0.13 and for alpha(s)=0.6, eta/s=0.076. The small eta/s values, which suggest strongly coupled systems, are due to the gluon bremsstrahlung incorporated.