Relativistic viscous hydrodynamics, conformal invariance, and holography

Abstract

We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled N=4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Mueller-Israel-Stewart theory, often used in numerical simulations, does not contain all allowed second-order terms and, frequently, terms required by conformal invariance.

32 pages, 1 figure; v2: references added; v3: typos corrected

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• Temperature in relativistic fluids
• Collective Expansion at the LHC: selected ALICE anisotropic flow measurements
• Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma
• Numerical Measurements of Scaling Relations in Two-Dimensional Conformal Fluid Turbulence
• An improved anisotropic hydrodynamics ansatz
• Viscous Cosmologies
• An AdS/CFT Connection between Boltzmann and Einstein
• Pseudo-rapidity distribution from a perturbative solution of viscous hydrodynamics for heavy ion collisions at RHIC and LHC
• Numerical evidence of electron hydrodynamic whirlpools in graphene samples
• Determination of the Shear Viscosity Relaxation Time at Weak and Strong Coupling
• A new relativistic hydrodynamics code for high-energy heavy-ion collisions
• The contribution of NLO and LPM corrections to thermal dilepton emission in heavy ion collisions
• The non-relativistic limit of first-order relativistic viscous fluids
• Electromagnetic quasinormal modes of rotating black strings and the AdS/CFT correspondence
• The Navier-Stokes equation and solution generating symmetries from holography
• Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids
• Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field
• Hydrodynamic attractor and novel fixed points in superfluid Bjorken flow
• Perturbation solutions of relativistic viscous hydrodynamics for longitudinally expanding fireballs
• Dissipative corrections to particle spectra and anisotropic flow from a saddle-point approximation to kinetic freeze out
• Universal chiral conductivities for low temperature holographic superfluids
• Fluid/gravity correspondence: A nonconformal realization in compactified D4 branes
• New insights into the analytic structure of correlation functions via kinetic theory
• Microcausality without Lorentz invariance
• Evaluating Results from the Relativistic Heavy Ion Collider with Perturbative QCD and Hydrodynamics
• Anomalies, Chern-Simons Terms and Black Hole Entropy
• Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions
• Antiscreening of the Ampere force in QED and QCD plasmas
• Casimir energy in the gauge/gravity description of Bjorken flow?
• Second order causal hydrodynamics in Eckart frame: using gradient expansion scheme
• Hydrodynamization times of a holographic fluid far from equilibrium
• Causality and stability analysis of first-order field redefinition in relativistic hydrodynamics from kinetic theory
• 4-point correlators in finite-temperature AdS/CFT: jet quenching correlations
• Near-Extremal Fluid Mechanics
• Branch-cut in the shear-stress response function of massless $\lambda {\phi }^4$ with Boltzmann statistics
• Homogeneous Relaxation at Strong Coupling from Gravity
• Non-conformal holographic Gauss-Bonnet hydrodynamics
• Second order equilibrium transport in strongly coupled $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills plasma via holography
• Nonlinear waves in second order conformal hydrodynamics
• Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions
• Understanding the holographic principle via RG flow
• Novel features of attractors and transseries in non-conformal Bjorken flows
• Conformal symmetry breaking in holographic QCD
• Relaxation Times for Chiral Transport Phenomena and Spin Polarization in Strongly Coupled Plasma
• Conserved and non-conserved Noether currents from the quantum effective action
• Quasinormal modes of NUT-charged black branes in the AdS/CFT correspondence
• Dispersion and suppression of sound near QCD critical point
• Second order relativistic viscous hydrodynamics within an effective description of hot QCD medium
• Universality Classes of Relativistic Fluid Dynamics: Applications
• Sensitivity of holographic $\mathcal{N}=4$ SYM plasma hydrodynamics to finite coupling corrections
• Infinite Order Hydrodynamics: An Analytical Example
• Field Theory Approaches to Relativistic Hydrodynamics
• Determining all thermodynamic transport coefficients for an interacting large N quantum field theory
• Transseries for causal diffusive systems
• Radiation in Fluid/Gravity and the Flat Limit
• Dual Fluid for the Kerr Black Hole
• Phenomenological Relativistic Second-Order Hydrodynamics for Multiflavor Fluids
• Cauchy Evolution of Asymptotically Global AdS Spacetimes with No Symmetries
• General relativistic non-ideal fluid equations for dark matter from a truncated cumulant expansion
• Scaling Relations in Two-Dimensional Relativistic Hydrodynamic Turbulence
• Random Fractal Ansatz for the configurations of Two-Dimensional Critical Systems
• Shocks in Quark-Gluon Plasmas
• Gauss-Bonnet AdS planar and spherical black hole thermodynamics and holography
• Klein-Gordon Equation in Hydrodynamical Form
• Upper Limit of Sound Speed in Nuclear Matter: A Harmonious Interplay of Transport Calculation and Perturbative Quantum Chromodynamic Constraint
• Conformal higher-order viscoelastic fluid mechanics
• Viscosity spectral function of a scale invariant non-relativistic fluid from holography
• On the Gravitational Wave to Matter Coupling of Superfluid Fermi Gases Near Unitarity
• Gravitation, Thermodynamics, and the Bound on Viscosity
• Anisotropic Flow and Jet Quenching in Relativistic Nuclear Collisions
• Geometric Josephson junction
• Hydrodynamization in hybrid Bjorken flow attractors
• Nonlinear evolution of density and flow perturbations on a Bjorken background
• Flat space compressible fluid as holographic dual of black hole with curved horizon
• A hydrodynamic approach to QGP instabilities
• Relativistic Viscous Hydrodynamics for Multi-Component Systems with Multiple Conserved Currents
• Comments on Entanglement Propagation
• First-order relativistic hydrodynamics with an information current
• Sum rules, plasma frequencies and Hall phenomenology in holographic plasmas
• Metric anisotropies and emergent anisotropic hydrodynamics
• Heat propagation in rotating relativistic bodies
• Free energy dependence on spatial geometry for (2+1)-dimensional QFTs
• Dynamical Friction in Interacting Relativistic Systems
• Dynamical spectral structure of density fluctuation near QCD critical point
• Dissipative Bjorken hydrodynamics from an AdS Schwarzschild black hole
• Mapping GENERIC hydrodynamics into Carter's multifluid theory
• Second order hydrodynamics based on effective kinetic theory and electromagnetic signals from QGP
• Causality and stability in first-order conformal anisotropic hydrodynamics
• Hydrodynamics in the Carrollian regime
• Causality Criteria from Stability Analysis at Ultra-High Boost
• Using the non-hydrodynamic mode to study the onset of hydrodynamic behavior in ultraperipheral symmetric nuclear collisions
• The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics
• Second order transport coefficients of nonconformal relativistic fluids in various dimensions from Dp-brane
• From Thermodynamics to the Bound on Viscosity
• Third order viscous hydrodynamics from the entropy four current
• Remarks on holographic models of the Kerr-AdS${}_5$ geometry
• Parity asymmetric boost invariant plasma in AdS/CFT correspondence
• Conductivity and quasinormal modes in holographic theories
• Noncovariant parabolic theories of relativistic diffusion
• Spectral BBGKY: a scalable scheme for nonlinear Boltzmann and correlation kinetics
• Holographic Constraints on Generalised Rivlin-Ericksen Fluid
• Second order transport coefficients of nonconformal fluids from compactified Dp-branes
• Anisotropic Flow and Viscous Hydrodynamics
• Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma
• Thermal backflow in CFTs
• Stabilization of the extended horizons
• Thermal photon production in Au+Au collisions: viscous corrections in two different hydrodynamic formalisms
• First-Order Viscous Relativistic Hydrodynamics on the Two-Sphere
• A derivation of the entropy-based relativistic smoothed particle hydrodynamics by variational principle
• Spin hydrodynamics -- recent developments
• Thermal dilepton production within conformal viscous Gubser flow
• Neutron star evolution with the Bemfica-Disconzi-Noronha-Kovtun viscous hydrodynamics framework
• Bottomonia in the Quark Gluon Plasma
• Constraint evolution in first-order viscous relativistic fluids
• Stable non-linear evolution in regularised higher derivative effective field theories
• Thermal Product Formula for Shear Modes
• Puzzles, Progress, Prospects: pre-Summary for the Quark Matter 2009 Conference
• Generalized relativistic second-order dissipative hydrodynamics: coupling different rank tensors
• Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach
• Viscosity bound versus the universal relaxation bound
• Correlation of density fluctuation in a magnetized QCD matter near the critical end point
• Small Amplitude Forced Fluid Dynamics from Gravity at T = 0
• On the boundary condition and related instability in the Smoothed Particle Hydrodynamics
• Microscopic Study of Vorticities in Relativistic Chiral Fermions
• Causal hydrodynamic fluctuations in a one-dimensional expanding system
• Causal and Stable Superfluid Hydrodynamics
• Non-conformal evolution of magnetic fields during reheating
• Compactified AdS black holes, Chamblin-Reall background, and their dual non-conformal relativistic fluids
• Projecting the likely importance of weak-interaction-driven bulk viscosity in neutron star mergers
• Hysteresis in $\eta /s$ for QFTs dual to spherical black holes
• Lifshitz hydrodynamics at generic $z$ from a moving black brane
• Superfluids in expanding backgrounds and attractor times
• Holographic approach to thermalization in general anisotropic theories
• Non-linear instability of slowly rotating Kerr-AdS black holes
• Higher-order anisotropic flow correlations in Xe-Xe collisions at $\sqrt{{\mathrm{s}}_{\mathrm{NN}}}=5.44TeV$
• Acausality-driven instabilities in transient relativistic viscous hydrodynamics
• Second order Galilean fluids & Stokes' law
• Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries
• Nonlinear analysis of causality for heat flow in heavy-ion collisions: constraints from equation of state
• Finite-time gradient blow-up and shock formation in Israel-Stewart theory: Bulk, shear, and diffusion regimes
• Inhomogeneous post-inflationary Lambda-CDM cosmology as a moduli space expansion
• Stability of 1+1 dimensional causal relativistic viscous hydrodynamics
• Nonlinear causality of Israel-Stewart theory with diffusion
• Rapidity Decorrelation from Hydrodynamic Fluctuations and Initial Fluctuations
• Lattice QCD and Hydro/Cascade Model of Heavy Ion Collisions
• Third-order dissipative hydrodynamics from the entropy principle
• Emergent Viscous Hydrodynamics From a Single Quantum Particle
• Hybrid thermalization in the large $N$ limit
• Hard gluon evolution in the last stage of the bottom-up thermalization
• Constraining the onset of viscous hydrodynamics
• Thermalization and Hydrodynamics of Two-Dimensional Quantum Field Theories
• Universal thermalization dynamics in (1+1)d QFTs
• Higher Spin Contributions to Holographic Fluid Dynamics in $Ad{S}_5/CF{T}_4$
• Gravitational susceptibility of QGP
• Compressible Fluids in the Membrane Paradigm: non-AdS Fluid/Gravity correspondences
• Memory Effects and Transport Coefficients for Non-Newtonian Fluids
• Nonperfect Carrollian Fluids Through Holography
• Conformal anomaly transport induced by dark photon
• The Wake of a Heavy Quark in Non-Abelian Plasmas : Comparing Kinetic Theory and the AdS/CFT Correspondence
• Gravitational reheating at strong coupling
• Time evolving fluid from Vaidya spacetime
• Hydrodynamics of holographic flavored plasmas
• Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution
• Extended applicability domain of viscous anisotropic hydrodynamics in (2+1)-D Bjorken flow with transverse expansion
• Hot Spaghetti: Viscous Gravitational Collapse
• The diffusion equation is compatible with special relativity
• Relativistic second-order dissipative hydrodynamics from Zubarev's non-equilibrium statistical operator
• Transport and response coefficients in second-order dissipative relativistic hydrodynamics with quantum corrections: probing the quark-gluon plasma
• Viscous Gubser flow with conserved charges to benchmark fluid simulations
• Magnetodynamic Characteristics and QGP Energy Dissipation in RMHD Framework with Relativistic Heavy-Ion Collisions