Effective actions for relativistic fluids from holography

TL;DR

The paper furnishes a holographic construction for the low-energy, dissipationless effective action of conformal fluids via a double Dirichlet problem in AdS gravity with UV and IR branes. It provides two complementary derivations: a nonlinear leading-order action derived from the full gravity solution and a linearized gravity-based action that clarifies the emergence of Goldstone modes corresponding to fluid degrees of freedom. By coupling to an IR sector either through the membrane paradigm or a Euclidean near-horizon sector, it demonstrates how dissipation or equilibrium partition functions arise, respectively, thereby clarifying the separation of dissipative and non-dissipative hydrodynamic behavior. The work also identifies the hydrodynamic entropy current as a Noether current of a symmetry acting on the Goldstone fields, linking holographic data to fundamental hydrodynamic constraints.

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.