Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics

Abstract

In ref. \cite{1406.7222}, we reported a construction of all order linearized fluid dynamics with strongly coupled $\mathcal{N}=4$ super-Yang-Mills theory as underlying microscopic description. The linearized fluid/gravity correspondence makes it possible to resum all order derivative terms in the fluid stress tensor. Dissipative effects are fully encoded by the shear term and a new one, emerging starting from third order in hydrodynamic derivative expansion. In this work, we provide all computational details omitted in \cite{1406.7222} and present additional results. We derive closed-form linear holographic RG flow-type equations for momenta-dependent transport coefficient functions. Generalized Navier-Stokes equations are shown to emerge from the constraint components of the bulk Einstein equations. We perturbatively solve the RG equations for the viscosity functions, up to third order in derivative expansion, and up to this order compute spectrum of small fluctuations. Finally, we solve the RG equations numerically, thus accounting for all order derivative terms in the boundary stress tensor.

v1: 33 pages, 4 multi-figures; v2: added 6 refs, made a couple of clarifications, to appear in JHEP; v3: corrected sound wave dispersion relation in equation (2.44)

References in corpus (62)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• A Stress Tensor for Anti-de Sitter Gravity
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Building an AdS/CFT superconductor
• The Holographic Weyl anomaly
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Nonlinear Fluid Dynamics from Gravity
• New Forms of QCD Matter Discovered at RHIC
• Full result for the QCD equation of state with 2+1 flavors
• The QCD equation of state with dynamical quarks
• From AdS/CFT correspondence to hydrodynamics
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• What RHIC Experiments and Theory tell us about Properties of Quark-Gluon Plasma ?
• Quasinormal modes and holography
• Viscosity Bound Violation in Higher Derivative Gravity
• Viscosity, Black Holes, and Quantum Field Theory
• Universality of the shear viscosity in supergravity
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Holographic and Wilsonian Renormalization Groups
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• The characteristics of thermalization of boost-invariant plasma from holography
• Asymptotic perfect fluid dynamics as a consequence of AdS/CFT
• Beyond eta/s = 1/4pi
• Holographic Superconductors with Higher Curvature Corrections
• Violation of the Holographic Viscosity Bound in a Strongly Coupled Anisotropic Plasma
• Hydrodynamic gradient expansion in gauge theory plasmas
• Does stability of relativistic dissipative fluid dynamics imply causality?
• Holographic Hydrodynamics with a Chemical Potential
• Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality
• Quantum corrections to eta/s
• Shear Viscosity from Effective Couplings of Gravitons
• A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Stability and Causality in relativistic dissipative hydrodynamics
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Viscous hydrodynamics relaxation time from AdS/CFT
• Wilsonian Approach to Fluid/Gravity Duality
• Universal holographic hydrodynamics at finite coupling
• Shear Viscosity from Gauss-Bonnet Gravity with a Dilaton Coupling
• Forced Fluid Dynamics from Gravity
• Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm
• Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant
• Non-universal shear viscosity from Einstein gravity
• Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT
• Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes
• Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory
• Deconstructing holographic liquids
• Universality of second order transport coefficients from the gauge-string duality
• How much entropy is produced in strongly coupled Quark-Gluon Plasma (sQGP) by dissipative effects?
• Higher derivative effects on eta/s at finite chemical potential
• Improved Hydrodynamics from the AdS/CFT
• All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence
• Holographic Wilsonian RG Flow and Sliding Membrane Paradigm
• Holographic Screens and Transport Coefficients in the Fluid/Gravity Correspondence
• Analytic Approaches to anisotropic Holographic Superfluids
• Proof of a universal lower bound on the shear viscosity to entropy density ratio
• Universal hydrodynamics and charged hadron multiplicity at the LHC

Cited by in corpus (40)

• New theories of relativistic hydrodynamics in the LHC era
• Fluid Dynamics far from Local Equilibrium
• A quantum hydrodynamical description for scrambling and many-body chaos
• The complex life of hydrodynamic modes
• Constructing higher-order hydrodynamics: The third order
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
• Thermoelectric conductivities, shear viscosity, and stability in an anisotropic linear axion model
• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
• Quasinormal modes in charged fluids at complex momentum
• Hydrodynamic gradient expansion in linear response theory
• A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
• Conductivities of magnetic quark-gluon plasma at strong coupling
• Fluid/gravity correspondence: Second order transport coefficients in compactified D4-branes
• Statistics of thermalization in Bjorken Flow
• All order effective action for charge diffusion from Schwinger-Keldysh holography
• Third-order relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma
• Linearly resummed hydrodynamics in a weakly curved spacetime
• Drag force to all orders in gradients
• The emergence of flagpole and flag-dipole fermions in fluid/gravity correspondence
• Relativistic Hydrodynamics: A Singulant Perspective
• Ginzburg-Landau effective action for a fluctuating holographic superconductor
• Anomalous transport from holography: Part II
• Anomalous transport from holography: Part I
• Nonlinear chiral transport from holography
• Aspects of univalence in holographic axion models
• Fluid/gravity correspondence for massive gravity
• Fluid/gravity correspondence and the CFM black brane solutions
• Gradient resummation for nonlinear chiral transport: an insight from holography
• Chiral transport in strong fields from holography
• Holographic Schwinger-Keldysh field theory of SU(2) diffusion
• Transseries for causal diffusive systems
• Chiral Anomalous Magnetohydrodynamics in action: effective field theory and holography
• Analytic structure of diffusive correlation functions
• $U(1)$ current from the AdS/CFT: diffusion, conductivity and causality
• Phase space holography with no strings attached
• Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence
• Sakai-Sugimoto Model in an Off-Shell: Chiral Lagrangian to All Orders
• Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation