Effective actions for relativistic fluids from holography

TL;DR

This paper derives a low energy, dissipationless effective action for strongly coupled conformal fluids using holography, employing novel double Dirichlet boundary conditions and geometric interpretations of Goldstone bosons.

Contribution

It introduces a holographic approach with double Dirichlet problems to formulate the effective action for relativistic fluids, linking boundary conditions to hydrodynamic modes.

Findings

Reproduces the dispersion relations for sound and shear waves.

Connects the effective action to the equilibrium partition function.

Defines the hydrodynamic entropy current as a Noether current.

Abstract

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.