$\eta/s$ at finite coupling

Abstract

We compute the ratio of the coefficient of shear viscosity to entropy density at finite coupling and at zero chemical potential using holographic duality up to ten derivative terms in the low energy effective 5-dimensional action, of a specific kind, which may or may not be connected to the supersymmetric completion of Type IIB theory. The result suggests that this ratio can be positive only for the 8th derivative term even with the form of that term in the action as ${{\cal C}^{ij}}_{kl}{{\cal C}^{kl}}_{mn}{{\cal C}^{mn}}_{rs}{{\cal C}^{rs}}_{ij}$, where ${\cal C}$ is the Weyl tensor.