From AdS/CFT correspondence to hydrodynamics

TL;DR

The paper tests the Minkowski-space AdS/CFT correspondence at finite temperature by computing real-time retarded Green's functions for R-current and stress-energy tensor operators in strongly coupled N=4 SYM. Using a non-extremal D3-brane background and a Minkowski prescription, it identifies hydrodynamic poles corresponding to R-charge diffusion and shear diffusion, obtaining a diffusion constant $D=1/(2\pi T)$ and a shear viscosity $\eta=\pi/8 \, N^2 T^3$. The results align with hydrodynamic expectations and with prior calculations from Kubo formulas and black-brane absorption, providing a nontrivial consistency check of the finite-temperature AdS/CFT framework. The work also establishes a concrete connection between gravity-mode perturbations and transport coefficients, with potential extensions to sound modes in future studies.

Abstract

We compute the correlation functions of R-charge currents and components of the stress-energy tensor in the strongly coupled large-N finite-temperature N=4 supersymmetric Yang-Mills theory, following a recently formulated Minkowskian AdS/CFT prescription. We observe that in the long-distance, low-frequency limit, such correlators have the form dictated by hydrodynamics. We deduce from the calculations the R-charge diffusion constant and the shear viscosity. The value for the latter is in agreement with an earlier calculation based on the Kubo formula and absorption by black branes.