  Motivated by the vast string landscape, we consider the shear viscosity to
entropy density ratio in conformal field theories dual to Einstein gravity with
curvature square corrections. After field redefinitions these theories reduce
to Gauss-Bonnet gravity, which has special properties that allow us to compute
the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning
of the coupling, the value of the shear viscosity to entropy density ratio can
be adjusted to any positive value from infinity down to zero, thus violating
the conjectured viscosity bound. At linear order in the coupling, we also check
consistency of four different methods to calculate the shear viscosity, and we
find that all of them agree. We search for possible pathologies associated with
this class of theories violating the viscosity bound.
