Hydrodynamics of strongly coupled non-conformal fluids from gauge/gravity duality

TL;DR

This paper uses gauge/gravity duality to analyze relativistic hydrodynamics of strongly coupled non-conformal fluids, deriving analytical dispersion relations for shear and sound modes without relying on the membrane paradigm.

Contribution

It provides new analytical solutions for shear and sound mode dispersion relations in non-conformal holographic fluids, including subleading terms, using gauge/gravity duality.

Findings

Analytical shear mode dispersion relation to order q^4

Analytical sound mode dispersion relation to order q^3

Subleading shear mode term analyzed without membrane paradigm

Abstract

The subject of relativistic hydrodynamics is explored using the tools of gauge/gravity duality. A brief literature review of AdS/CFT and gauge/gravity duality is presented first. This is followed by a pedagogical introduction to the use of these methods in determining hydrodynamic dispersion relations, $w(q)$, of perturbations in a strongly coupled fluid. Shear and sound mode perturbations are examined in a special class of gravity duals: those where the matter supporting the metric is scalar in nature. Analytical solutions (to order $q^4$ and $q^3$ respectively) for the shear and sound mode dispersion relations are presented for a subset of these backgrounds. The work presented here is based on previous publications by the same author, though some previously unpublished results are also included. In particular, the subleading term in the shear mode dispersion relation is analyzed using the AdS/CFT correspondence without any reference to the black hole membrane paradigm.