Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon

TL;DR

This paper demonstrates how holographic RG flow can be used to reconstruct spacetime from boundary hydrodynamics, specifically linking the emergence of spacetime to the non-relativistic Navier-Stokes equations at the horizon.

Contribution

It provides a precise formulation of holographic RG flow that allows spacetime to be reconstructed without explicit bulk metric knowledge, connecting horizon fluid dynamics to spacetime emergence.

Findings

Spacetime can be reconstructed from RG flow equations.

Horizon fluid fixed point leads to Navier-Stokes dynamics.

Transport coefficients are determined independently of asymptotic values.

Abstract

We show that holographic RG flow can be defined precisely such that it corresponds to emergence of spacetime. We consider the case of pure Einstein's gravity with a negative cosmological constant in the dual hydrodynamic regime. The holographic RG flow is a system of first order differential equations for radial evolution of the energy-momentum tensor and the variables which parametrize it's phenomenological form on hypersurfaces in a foliation. The RG flow can be constructed without explicit knowledge of the bulk metric provided the hypersurface foliation is of a special kind. The bulk metric can be reconstructed once the RG flow equations are solved. We show that the full spacetime can be determined from the RG flow by requiring that the horizon fluid is a fixed point in a certain scaling limit leading to the non-relativistic incompressible Navier-Stokes dynamics. This restricts the near-horizon forms of all transport coefficients, which are thus determined independently of their asymptotic values and the RG flow can be solved uniquely. We are therefore able to recover the known boundary values of almost all transport coefficients at the first and second orders in the derivative expansion. We conjecture that the complete characterisation of the general holographic RG flow, including the choice of counterterms, might be determined from the hydrodynamic regime.