$\eta/s$ at finite coupling

TL;DR

This paper calculates the shear viscosity to entropy density ratio at finite coupling using holographic duality, considering higher derivative corrections up to ten derivatives in the effective 5D action, revealing conditions for positivity.

Contribution

It provides a detailed computation of the $rac{ ext{shear viscosity}}{ ext{entropy density}}$ ratio at finite coupling including up to ten derivative terms, highlighting the specific form that affects positivity.

Findings

The ratio can be positive only for the 8th derivative term.

The form of the correction term significantly influences the ratio's positivity.

Higher derivative terms beyond the 8th derivative do not yield positive ratios.

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.