A Holographic Dual of Hydrodynamics

TL;DR

The paper develops a holographic dual for a time-dependent, strongly coupled N=4 SYM fluid undergoing Bjorken expansion with shear viscosity. Using Fefferman-Graham holography and late-time expansions, it derives a viscous bulk geometry whose horizon encodes integration constants not fixed by hydrodynamics, and demonstrates consistency with dissipative Bjorken flow while reproducing Stefan-Boltzmann scaling in the strongly coupled regime. A key result is the viscous correction to the energy density, rho(τ) ≈ ρ0/τ^(4/3) − 2η0/τ^2, and a horizon-determined entropy S∞, showing holography provides deeper insight into non-equilibrium dynamics than hydrodynamics alone. The analysis confirms regularity of the bulk geometry for a physically relevant range of viscous exponents and points to extensions to more general expansions and non-conformal cases relevant to RHIC physics.

Abstract

We consider a gravity dual description of time dependent, strongly interacting large-Nc N=4 SYM. We regard the gauge theory system as a fluid with shear viscosity. Our fluid is expanding in one direction following the Bjorken's picture that is relevant to RHIC experiments. We obtain the dual geometry at the late time that is consistent with dissipative hydrodynamics. We show that the integration constants that cannot be determined by hydrodynamics are given by looking at the horizon of the dual geometry. Relationship between time dependence of the energy density and bulk singularity is also discussed.