Conformal non-relativistic hydrodynamics from gravity

TL;DR

This work extends the fluid-gravity correspondence to conformal non-relativistic field theories with Schrödinger symmetry by combining light-cone reduction of relativistic fluids with TsT-generated bulk geometries. It shows that holographic duals of these non-relativistic CFTs behave hydrodynamically at long distances and provides the gravitational construction for inhomogeneous fluid flows. A key result is the expression for thermal conductivity in terms of relativistic transport, which leads to a unity Prandtl number in the planar limit. The approach leverages the DLCQ framework and emphasizes that the hydrodynamic data of the non-relativistic theory can be read from the relativistic parent theory, either directly or via TsT transformations. Overall, the paper solidifies the holographic understanding of non-relativistic conformal fluids and highlights avenues for exploring higher-order transport and incompressible limits.

Abstract

We show that the recently constructed holographic duals of conformal non-relativistic theories behave hydrodynamically at long distances, and construct the gravitational dual of fluid flows in a long-wavelength approximation. We compute the thermal conductivity of the holographic conformal non-relativistic fluid. The corresponding Prandtl number is equal to one.