Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

Abstract

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the non-relativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

4 pages

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• Particles and fields in fluid turbulence
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• Relativistic viscous hydrodynamics, conformal invariance, and holography
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Cited by in corpus (50)

• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Galilean Conformal Algebras and AdS/CFT
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• GCA in 2d
• From Navier-Stokes To Einstein
• Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• The holographic fluid dual to vacuum Einstein gravity
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces
• Navier-Stokes Equations on Black Hole Horizons and DC Thermoelectric Conductivity
• DC Conductivity of Magnetised Holographic Matter
• Conformal non-relativistic hydrodynamics from gravity
• Sound modes in holographic superfluids
• Non-relativistic conformal symmetries in fluid mechanics
• Limitations of Pseudo-Newtonian approach in studying the accretion flow around Kerr black hole
• Relativistic CFT Hydrodynamics from the Membrane Paradigm
• The Relativistic Rindler Hydrodynamics
• The relativistic fluid dual to vacuum Einstein gravity
• Supersymmetric Extension of GCA in 2d
• Causality and the AdS Dirichlet problem
• Phenomenology of non-relativistic parity-violating hydrodynamics in 2+1 dimensions
• Non-Relativistic Parity-Violating Hydrodynamics in Two Spatial Dimensions
• Holographic Forced Fluid Dynamics in Non-relativistic Limit
• CFT Hydrodynamics: Symmetries, Exact Solutions and Gravity
• Holographic Non-Abelian Charged Hydrodynamics from the Dynamics of Null Horizons
• Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence
• Hydrodynamics from the D1-brane
• Bifurcation of Plasma Balls and Black Holes to Lobed Configurations
• Exact Scaling Relations In Relativistic Hydrodynamic Turbulence
• Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon
• Higher Curvature Gravity and the Holographic fluid dual to flat spacetime
• Extremal black holes, Holography & Coarse graining
• Conformal symmetry and non-relativistic second order fluid dynamics
• Holographic Vorticity in the Fluid/Gravity Correspondence
• The Penrose Inequality and the Fluid/Gravity Correspondence
• Phase diagram for non-axisymmetric plasma balls
• Numerical Measurements of Scaling Relations in Two-Dimensional Conformal Fluid Turbulence
• Vortices in (2+1)d Conformal Fluids
• Fluid Super-Dynamics from Black Hole Superpartners
• Supersymmetric Fluid Dynamics
• String Theory: A Framework for Quantum Gravity and Various Applications
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Galilean Conformal Algebra in Semi-Infinite Space
• One-Dimensional Approximation of Viscous Flows
• A hydrodynamical description of gravitational waves
• Holographic Hydrodynamics and Applications to RHIC and LHC
• Relativistic Holographic Hydrodynamics from Black Hole Horizons
• DC conductivities and Stokes flows in Dirac semimetals
• Fluid/Gravity Correspondence with Scalar Field and Electromagnetic Field