Causal three-point functions and nonlinear second-order hydrodynamic coefficients in AdS/CFT

In the context of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = {4} $\end{document} SYM, we compute the finite ’t Hooft coupling λ correction to the non-linear second-order hydrodynamic coefficient λ3 from a Kubo formula based on fully retarded three-point functions using AdS/CFT. Although λ3 is known to vanish in the infinite ’t Hooft coupling limit, we find that the finite λ correction is non-zero. We also present a set of Kubo formulae for the non-linear coefficients λ1,2,3, which is more convenient than the one that has appeared recently elsewhere.