Effective actions for relativistic fluids from holography

  • Jan de Boer
  • Michal P. Heller
  • Natalia Pinzani-Fokeeva
Open Access
Regular Article - Theoretical Physics


Motivated by recent progress in developing action formulations of relativistic hydrodynamics, we use holography to derive the low energy dissipationless effective action for strongly coupled conformal fluids. Our analysis is based on the study of novel double Dirichlet problems for the gravitational field, in which the boundary conditions are set on two codimension one timelike hypersurfaces (branes). We provide a geometric interpretation of the Goldstone bosons appearing in such constructions in terms of a family of spatial geodesics extending between the ultraviolet and the infrared brane. Furthermore, we discuss supplementing double Dirichlet problems with information about the near-horizon geometry. We show that upon coupling to a membrane paradigm boundary condition, our approach reproduces correctly the complex dispersion relation for both sound and shear waves. We also demonstrate that upon a Wick rotation, our formulation reproduces the equilibrium partition function formalism, provided the near- horizon geometry is properly accounted for. Finally, we define the conserved hydrodynamic entropy current as the Noether current associated with a particular transformation of the Goldstone bosons.


AdS-CFT Correspondence Effective field theories 


Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Jan de Boer
    • 1
  • Michal P. Heller
    • 2
  • Natalia Pinzani-Fokeeva
    • 1
  1. 1.Institute of PhysicsUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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