All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence

TL;DR

This paper uses fluid/gravity correspondence to derive all-order linearized hydrodynamics for strongly coupled $ ext{N}=4$ super-Yang-Mills theory, including new dissipative effects and momentum-dependent viscosity functions.

Contribution

It introduces the first closed-form holographic RG flow equations for generalized viscosity functions at all orders in derivatives.

Findings

Derived stress tensor up to third order analytically.

Numerically computed viscosity functions at large momenta.

Validated results by deriving generalized Navier-Stokes equations.

Abstract

Using fluid/gravity correspondence, we determine the (linearized) stress energy tensor of $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling with all orders in derivatives of fluid velocity included. We find that the dissipative effects are fully encoded in the shear term and a new one, which emerges starting from the third order. We derive, for the first time, closed linear holographic RG flow-type equations for (generalized) momenta-dependent viscosity functions. In the hydrodynamic regime, we obtain the stress tensor up to third order in derivative expansion analytically. We then numerically determine the viscosity functions up to large momenta. As a check of our results, we also derive the generalized Navier-Stokes equations from the Einstein equations in the dual gravity.