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

TL;DR

This paper calculates the finite 't Hooft coupling correction to a specific second-order hydrodynamic coefficient in N=4 SYM using AdS/CFT, revealing a non-zero correction where it previously vanished.

Contribution

It introduces a new set of Kubo formulas for nonlinear hydrodynamic coefficients and computes the finite coupling correction to , which was previously known to vanish at infinite coupling.

Findings

Finite  correction is non-zero at finite .

New Kubo formulas for , ,  are proposed.

Provides insights into nonlinear hydrodynamics in strongly coupled gauge theories.

Abstract

In the context of $\mathcal{N}=4$ SYM, we compute the finite 't Hooft coupling $\lambda$ correction to the non-linear second-order hydrodynamic coefficient $\lambda_3$ from a Kubo formula based on fully retarded three-point functions using AdS/CFT. Although $\lambda_3$ is known to vanish in the infinite 't Hooft coupling limit, we find that the finite $\lambda$ correction is non-zero. We also present a set of Kubo formulae for the non-linear coefficients $\lambda_{1,2,3}$, which is more convenient than the one that has appeared recently elsewhere.