Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in ultraviolet-complete theories with a gravity dual

Abstract

We reconsider, from a novel perspective, how unitarity constrains the corrections to the ratio of shear viscosity \eta\ to entropy density s. We start with higher-derivative extensions of Einstein gravity in asymptotically anti-de Sitter spacetimes. It is assumed that these theories are derived from string theory and thus have a unitary UV completion that is dual to a unitary, UV-complete boundary gauge theory. We then propose that the gravitational perturbations about a solution of the UV complete theory are described by an effective theory whose linearized equations of motion have at most two time derivatives. Our proposal leads to a concrete prescription for the calculation of \eta/s for theories of gravity with arbitrary higher-derivative corrections. The resulting ratio can take on values above or below 1/4\pi\ and is consistent with all the previous calculations, even though our reasoning is substantially different. For the purpose of calculating \eta/s, our proposal also leads to only two possible candidates for the effective two-derivative theory: Einstein and Gauss-Bonnet gravity. The distinction between the two is that Einstein gravity satisfies the equivalence principle, and so its graviton correlation functions are polarization independent, whereas the Gauss-Bonnet theory has polarization-dependent correlation functions. We discuss the graviton three-point functions in this context and explain how these can provide additional information on the value of \eta/s.