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Freelance Fluid/Gravity Correspondence, 3d Analysis

M. M. Sheikh-Jabbari, V. Taghiloo

TL;DR

This work extends the gauge/gravity duality to a freelance fluid/gravity framework in AdS$_3$ by allowing arbitrary timelike boundaries and boundary conditions. Leveraging the integrable nature of 3D gravity and Fefferman–Graham holography, it constructs a precise RG-flow description for the fluid variables, proves a $v_g$-theorem guaranteeing subluminal sound propagation toward the IR, and maps asymptotic fluids to finite-cutoff hydro-gravitational systems under general boundary conditions. It provides exact interpolation formulas for the induced metric and stress tensor across radii, and analyzes multiple boundary-condition families (Dirichlet, Neumann, conformal, CSS), with explicit finite-cutoff fluid expressions and group/phase velocities. The results illuminate how the fluid description dynamically couples to gravity at finite cutoff and offer a controlled arena to study holographic RG flows and hydrodynamics beyond the standard Dirichlet setup, with potential extensions to higher dimensions and dynamical boundary gravity. Overall, the framework unifies holographic fluid dynamics with boundary-condition freedom and RG structure, advancing the understanding of hydro-gravitational systems in holography.

Abstract

Freelance holography program is an extension of gauge/gravity correspondence, where the gravity theory is defined on a portion of AdS with an arbitrary timelike boundary, with any desired boundary conditions. It is also known that gauge/gravity correspondence admits a fluid/gravity correspondence limit, where the gauge theory side is well described by a fluid. In this work, combining the two, we work through ``freelance fluid/gravity''. In particular, we study in detail the 2d fluid (3d Einstein gravity) case, where one has a good analytical control over the bulk equations due to their integrability and absence of viscosity in the 2d fluid. We study consistency and validity requirements for the freelance fluid/gravity and how the fluid changes along the renormalization group (RG) flow. We prove the $v_g$-theorem, stating that the group velocity of fluid waves $v_g$ is a decreasing function as we move toward the infrared region along the RG flow, regardless of the adopted boundary conditions. We also study examples of holographic fluid with various asymptotic boundary conditions.

Freelance Fluid/Gravity Correspondence, 3d Analysis

TL;DR

This work extends the gauge/gravity duality to a freelance fluid/gravity framework in AdS by allowing arbitrary timelike boundaries and boundary conditions. Leveraging the integrable nature of 3D gravity and Fefferman–Graham holography, it constructs a precise RG-flow description for the fluid variables, proves a -theorem guaranteeing subluminal sound propagation toward the IR, and maps asymptotic fluids to finite-cutoff hydro-gravitational systems under general boundary conditions. It provides exact interpolation formulas for the induced metric and stress tensor across radii, and analyzes multiple boundary-condition families (Dirichlet, Neumann, conformal, CSS), with explicit finite-cutoff fluid expressions and group/phase velocities. The results illuminate how the fluid description dynamically couples to gravity at finite cutoff and offer a controlled arena to study holographic RG flows and hydrodynamics beyond the standard Dirichlet setup, with potential extensions to higher dimensions and dynamical boundary gravity. Overall, the framework unifies holographic fluid dynamics with boundary-condition freedom and RG structure, advancing the understanding of hydro-gravitational systems in holography.

Abstract

Freelance holography program is an extension of gauge/gravity correspondence, where the gravity theory is defined on a portion of AdS with an arbitrary timelike boundary, with any desired boundary conditions. It is also known that gauge/gravity correspondence admits a fluid/gravity correspondence limit, where the gauge theory side is well described by a fluid. In this work, combining the two, we work through ``freelance fluid/gravity''. In particular, we study in detail the 2d fluid (3d Einstein gravity) case, where one has a good analytical control over the bulk equations due to their integrability and absence of viscosity in the 2d fluid. We study consistency and validity requirements for the freelance fluid/gravity and how the fluid changes along the renormalization group (RG) flow. We prove the -theorem, stating that the group velocity of fluid waves is a decreasing function as we move toward the infrared region along the RG flow, regardless of the adopted boundary conditions. We also study examples of holographic fluid with various asymptotic boundary conditions.
Paper Structure (34 sections, 99 equations, 1 figure)

This paper contains 34 sections, 99 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Organization of the paper.
  3. Preliminaries
  4. AdS3 gravity
  5. Geometric setup.
  6. Notation.
  7. AdS$_3$ Einstein gravity action.
  8. Integrating radial bulk evolution.
  9. Radial flow of the solution phase space
  10. Freelance fluid/gravity correspondence: Various asymptotic boundary conditions
  11. Asymptotic boundary conditions
  12. Asymptotic constraints
  13. Asymptotic fluid
  14. Fluid in null frame and null fluids.
  15. Discriminant of timelike and null fluids.
  16. ...and 19 more sections

Figures (1)

  • Figure 1: Asymptotically AdS$_3$ spacetime and a region cutoff at radius $r$. $\textcolor{black}{\cal{M}}$ denotes the global asymptotically AdS$_3$ spacetime and $\textcolor{blue!80}{\Sigma}$ is its asymptotic timelike boundary. The shaded region $\textcolor{blue!50!black}{\mathcal{M}_r}$ is the part of AdS$_3$ cutoff at radius $r$, enclosed in a timelike surface $\textcolor{darkred!60}{\Sigma_r}$.