Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT

TL;DR

The paper addresses how second-order holographic hydrodynamics depends on spacetime dimension for conformal fluids with AdS$_D$ duals ($D\in\{3,4,5,6,7\}$). It extends the derivative-expansion approach to general $D$, solving Einstein equations in Eddington–Finkelstein coordinates and extracting the boundary stress tensor via the Brown–York prescription, fixing zero-momentum modes with a Landau-frame holographic condition. The authors obtain explicit expressions for the second-order transport coefficients $\eta$, $\tau_{\Pi}$, and $\lambda_i$, confirming the universal strong-coupling result $\eta/s = 1/(4\pi)$ and detailing how these coefficients behave in different dimensions, with $D=3$ yielding an exact AdS$_3$ black hole dual to a 1+1D perfect fluid. They also show that the $AdS_3$ case maps to the static BTZ black hole via a coordinate transformation, highlighting the special role of low dimensions in holographic hydrodynamics.

Abstract

We compute coefficients of two-derivative terms in the hydrodynamic energy momentum tensor of a viscous fluid which has an AdS_D dual with D between 3 and 7. For the case of D=3 we obtain an exact AdS_3 black hole solution, valid to all orders in a derivative expansion, dual to a perfect fluid in 1+1 dimensions.