Heavy quark potential as a function of shear viscosity at strong coupling

We determine finite temperature corrections to the heavy-quark (static) potential as a function of the shear viscosity-to-entropy density ratio in a strongly coupled, large-Nc conformal field theory dual to five-dimensional Gauss-Bonnet gravity. We find that these corrections are even smaller than those predicted by perturbative QCD at distances relevant for small bound states in a deconfined plasma. Obtaining the dominant temperature and viscosity dependence of quarkonium binding energies will require a theory where conformal invariance is broken in such a way that the free energy associated with a single heavy quark is not just a pure entropy contribution.