Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity

We discuss corrections to the ratio of shear viscosity to entropy density $\eta/s$ in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative corrections to Einstein gravity, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio $\eta/s$ remains at the Einstein-gravity value of $1/4\pi$ to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative theories, $\eta/s$ can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. Our findings provide further evidence for the validity of the KSS bound. In an appendix, the particular case of Gauss-Bonnet gravity is discussed.