The transport coefficients of strongly interacting matter are currently subject of intense theoretical and phenomenological studies due to their relevance for the characterization of the quark-gluon plasma produced in ultra-relativistic heavy-ion collisions (uRHIC). We discuss the connection between the shear viscosity to entropy density ratio, η/s, and the electric conductivity, σ el . We note that once the relaxation time is tuned to determine the shear viscosity η to have a minimum value η/s

more »

... = 1/4π near the critical temperature T c , one simultaneously predicts an electric conductivity σ el /T very close to recent lQCD data. More generally, we discuss why the ratio of η/s over σ el /T supplies a measure of the quark to gluon scattering rates whose knowledge would allow to significantly advance in the understanding of the QGP phase. We also predict that (η/s)/(σ el /T ), independently on the running coupling α s (T ), should increase up to about ∼ 20 for T → T c , while it goes down to a nearly flat behavior around 4 for T ≥ 4 T c .