On the universal hydrodynamics of strongly coupled CFTs with gravity duals

TL;DR

This paper demonstrates that classical 5D gravity solutions with AdS asymptotics can uniquely encode the hydrodynamics of strongly coupled 4D CFTs, revealing conditions for regular, singularity-free configurations and constructing explicit solutions.

Contribution

It introduces a method to construct and analyze hydrodynamic solutions in Fefferman-Graham coordinates, ensuring regularity and uniqueness, and explores their implications for dual CFTs.

Findings

Solutions have integer Taylor series in radial coordinate with no log terms.

Regular solutions correspond to specific hydrodynamic stress tensors without naked singularities.

Explicit first-order solutions are provided for arbitrary shear viscosity to entropy ratio.

Abstract

It is known that the solutions of pure classical 5D gravity with $AdS_5$ asymptotics can describe strongly coupled large N dynamics in a universal sector of 4D conformal gauge theories. We show that when the boundary metric is flat we can uniquely specify the solution by the boundary stress tensor. We also show that in the Fefferman-Graham coordinates all these solutions have an integer Taylor series expansion in the radial coordinate (i.e. no $log$ terms). Specifying an arbitrary stress tensor can lead to two types of pathologies, it can either destroy the asymptotic AdS boundary condition or it can produce naked singularities. We show that when solutions have no net angular momentum, all hydrodynamic stress tensors preserve the asymptotic AdS boundary condition, though they may produce naked singularities. We construct solutions corresponding to arbitrary hydrodynamic stress tensors in Fefferman-Graham coordinates using a derivative expansion. In contrast to Eddington-Finkelstein coordinates here the constraint equations simplify and at each order it is manifestly Lorentz covariant. The regularity analysis, becomes more elaborate, but we can show that there is a unique hydrodynamic stress tensor which gives us solutions free of naked singularities. In the process we write down explicit first order solutions in both Fefferman-Graham and Eddington-Finkelstein coordinates for hydrodynamic stress tensors with arbitrary $\eta/s$. Our solutions can describe arbitrary (slowly varying) velocity configurations. We point out some field-theoretic implications of our general results.