CFT Hydrodynamics: Symmetries, Exact Solutions and Gravity

Abstract

We consider the hydrodynamics of relativistic conformal field theories at finite temperature and its slow motions limit, where it reduces to the incompressible Navier-Stokes equations. The symmetries of the equations and their solutions are analyzed. We construct exact solutions with finite time singularities of one-dimensional relativistic conformal hydrodynamic motions, and use them to generate multi-dimensional solutions via special conformal transformations. These solutions, however, are shown to have no non-trivial slow motions limit. A simple non-equilibrium steady state in the form of a shock solution is constructed, and its inner structure is analyzed. We demonstrate that the derivation of the gravitational dual description of conformal hydrodynamics is analogous to the derivation of hydrodynamics equations from the Boltzmann equation. The shock solution is shown to correspond to a domain-wall solution in gravity. We show that the solutions to the non-relativistic incompressible Navier-Stokes equations play a special role in the construction of global solutions to gravity.

17 pages

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• Large N Field Theories, String Theory and Gravity
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Cited by in corpus (22)

• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Galilean Conformal Algebras and AdS/CFT
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• From Navier-Stokes To Einstein
• Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
• Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• Comments on Galilean conformal field theories and their geometric realization
• Non-relativistic conformal symmetries in fluid mechanics
• Relativistic CFT Hydrodynamics from the Membrane Paradigm
• Gravitational quasinormal modes of AdS black branes in d spacetime dimensions
• Supersymmetric Extension of GCA in 2d
• Holographic Heavy-Ion Collisions: Analytic Solutions with Longitudinal Flow, Elliptic Flow and Vorticity
• Exact analytical solutions of second-order conformal hydrodynamics
• Holographic Non-Abelian Charged Hydrodynamics from the Dynamics of Null Horizons
• A systematic study of exact solutions in second-order conformal hydrodynamics
• Shock waves in strongly coupled plasmas
• A Covariant Form of the Navier-Stokes Equation for the Galilean Conformal Algebra
• The group-theoretic approach to perfect fluid equations with conformal symmetry
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• The Penrose Inequality and the Fluid/Gravity Correspondence
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry