CFT hydrodynamics: Symmetries, exact solutions and gravity

Itzhak Fouxon*, Yaron Oz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

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.

Original languageEnglish
Article number120
JournalJournal of High Energy Physics
Volume2009
Issue number3
DOIs
StatePublished - 2009

Keywords

  • AdS-CFT correspondence
  • Classical theories of gravity
  • Gauge-gravity correspondence

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