TY - JOUR
T1 - CFT hydrodynamics
T2 - Symmetries, exact solutions and gravity
AU - Fouxon, Itzhak
AU - Oz, Yaron
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - AdS-CFT correspondence
KW - Classical theories of gravity
KW - Gauge-gravity correspondence
UR - http://www.scopus.com/inward/record.url?scp=67650255041&partnerID=8YFLogxK
U2 - 10.1088/1126-6708/2009/03/120
DO - 10.1088/1126-6708/2009/03/120
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AN - SCOPUS:67650255041
SN - 1126-6708
VL - 2009
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 3
M1 - 120
ER -