Off-shell hydrodynamics from holography

TL;DR

This paper proposes a holographic approach to derive an off-shell action principle for non-dissipative fluid dynamics by integrating out bulk gravitational degrees of freedom, leading to a novel formulation involving boundary-horizon embeddings.

Contribution

It introduces a new holographic method to formulate ideal fluid dynamics through an off-shell action based on boundary-horizon hypersurface embeddings.

Findings

Reduces to Dubovsky et al.'s ideal fluid action at zeroth order

Provides a holographic framework for off-shell hydrodynamics

Links bulk gravitational dynamics to boundary fluid variables

Abstract

We outline a program for obtaining an action principle for dissipative fluid dynamics by considering the holographic Wilsonian renormalization group applied to systems with a gravity dual. As a first step, in this paper we restrict to systems with a non-dissipative horizon. By integrating out gapped degrees of freedom in the bulk gravitational system between an asymptotic boundary and a horizon, we are led to a formulation of hydrodynamics where the dynamical variables are not standard velocity and temperature fields, but the relative embedding of the boundary and horizon hypersurfaces. At zeroth order, this action reduces to that proposed by Dubovsky et al. as an off-shell formulation of ideal fluid dynamics.