Abstract
We consider long wavelength solutions to the Einstein-dilaton system with negative cosmological constant which are dual, under the AdS/CFT correspondence, to solutions of the conformal relativistic Navier-Stokes equations with a dilaton-dependent forcing term. Certain forced fluid flows are known to exhibit turbulence; holographic duals of forced fluid dynamics are therefore of particular interest as they may aid efforts towards an explicit model of holographic steady state turbulence. In recent work, Bhattacharyya et al. have constructed long wavelength asymptotically locally AdS5 bulk space-times with a slowly varying boundary dilaton field which are dual to forced fluid flows on the 4–dimensional boundary. In this paper, we generalise their work to arbitrary space-time dimensions; we explicitly compute the dual bulk metric, the fluid dynamical stress tensor and Lagrangian to second order in a boundary derivative expansion.
Highlights
A perturbative constructionWe have established that the Einstein equations with negative cosmological constant provide the dual dynamics of the stress tensor for an infinite class of strongly coupled field theories; and that if we are aiming to construct analytic, time-dependent holographic bulk solutions describing interesting, non-trivial, non-equilibrium phenomena, fluid dynamics may well be a promising place to start
Considerable progress has already been made in obtaining the holographic duals of equilibrium field theory configurations
If we are motivated by the desire to obtain analytically the holographic dual of a certain class of interesting, non-trivial non-equilibrium phenomena, a natural starting point would be fluid dynamics
Summary
We have established that the Einstein equations with negative cosmological constant provide the dual dynamics of the stress tensor for an infinite class of strongly coupled field theories; and that if we are aiming to construct analytic, time-dependent holographic bulk solutions describing interesting, non-trivial, non-equilibrium phenomena, fluid dynamics may well be a promising place to start. This intuition was spectacularly confirmed in [16]. To fluid dynamics, we should be aiming to solve the Einstein equations perturbatively to some specified accuracy in the boundary derivative expansion
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