On the universal identity in second order hydrodynamics

Abstract

We compute the 't Hooft coupling correction to the infinite coupling expression for the second order transport coefficient ${\lambda }_2$ in $\mathcal{N}=4$ $SU(N_c)$ supersymmetric Yang-Mills theory at finite temperature in the limit of infinite $N_c$, which originates from the $R^4$ terms in the low energy effective action of the dual type IIB string theory. Using this result, we show that the identity involving the three second order transport coefficients, $2\eta {\tau }_{\Pi }-4{\lambda }_1-{\lambda }_2=0$, previously shown by Haack and Yarom to hold universally in relativistic conformal field theories with string dual descriptions to leading order in supergravity approximation, holds also at next to leading order in this theory. We also compute corrections to transport coefficients in a (hypothetical) strongly interacting conformal fluid arising from the generic curvature squared terms in the corresponding dual gravity action (in particular, Gauss-Bonnet action), and show that the identity holds to linear order in the higher-derivative couplings. We discuss potential implications of these results for the near-equilibrium entropy production rate at strong coupling.

V2: 16 pages, references added; V3: 16 pages, Published version with one additional reference

References in corpus (23)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Nonlinear Fluid Dynamics from Gravity
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Viscosity, Black Holes, and Quantum Field Theory
• Viscosity Bound and Causality Violation
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Bulk viscosity of gauge theory plasma at strong coupling
• The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
• Second order hydrodynamic coefficients from kinetic theory
• Adiabatic hydrodynamics: The eightfold way to dissipation
• Resolving disagreement for eta/s in a CFT plasma at finite coupling
• Universal holographic hydrodynamics at finite coupling
• Kubo Formulae for Second-Order Hydrodynamic Coefficients
• Shear viscosity in weakly coupled $\mathcal{N}=4$ Super Yang-Mills theory compared to QCD
• Shear viscosity of boost invariant plasma at finite coupling
• The eightfold way to dissipation
• Quasinormal spectrum and the black hole membrane paradigm
• Relaxation time of a CFT plasma at finite coupling
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Second order hydrodynamics of a CFT plasma from boost invariant expansion
• An elementary stringy estimate of transport coefficients of large temperature QCD
• Holographic real-time non-relativistic correlators at zero and finite temperature
• A breakdown of a universal hydrodynamic relation in Gauss-Bonnet gravity

Cited by in corpus (49)

• Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
• Black hole scrambling from hydrodynamics
• Weak Quantum Chaos
• Adiabatic hydrodynamics: The eightfold way to dissipation
• Holography and hydrodynamics with weakly broken symmetries
• Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current
• Constructing higher-order hydrodynamics: The third order
• From strong to weak coupling in holographic models of thermalization
• Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid
• On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
• Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma
• All higher-curvature gravities as Generalized quasi-topological gravities
• Holographic studies of Einsteinian cubic gravity
• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• Coupling constant corrections in a holographic model of heavy ion collisions
• Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration
• Shear viscosity in holography and effective theory of transport without translational symmetry
• Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
• Finite coupling corrections to holographic predictions for hot QCD
• A panoply of Schwinger-Keldysh transport
• Holographic Isotropisation in Gauss-Bonnet Gravity
• Second-Order Hydrodynamics and Universality in Non-Conformal Holographic Fluids
• Transport peak in thermal spectral function of $\mathcal{N}=4$ supersymmetric Yang-Mills plasma at intermediate coupling
• Fluid/gravity correspondence: Second order transport coefficients in compactified D4-branes
• Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity
• A Computer Test of Holographic Flavour Dynamics
• Hydrodynamic dispersion relations at finite coupling
• Adding new branches to the "Christmas tree" of the quasinormal spectrum of black branes
• Universality of anomalous conductivities in theories with higher-derivative holographic duals
• Holographic Zero Sound from Spacetime-Filling Branes
• Coupling Constant Corrections in a Holographic Model of Heavy Ion Collisions with Nonzero Baryon Number Density
• Holographic constraints on Bjorken hydrodynamics at finite coupling
• Analytic Transport from Weak to Strong Coupling in the O(N) model
• Shear Viscosity to Entropy Density Ratio in Higher Derivative Gravity with Momentum Dissipation
• Fluid/gravity correspondence and the CFM black brane solutions
• Second order equilibrium transport in strongly coupled $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills plasma via holography
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• Determining all thermodynamic transport coefficients for an interacting large N quantum field theory
• Sensitivity of holographic $\mathcal{N}=4$ SYM plasma hydrodynamics to finite coupling corrections
• A breakdown of a universal hydrodynamic relation in Gauss-Bonnet gravity
• On the Gravitational Wave to Matter Coupling of Superfluid Fermi Gases Near Unitarity
• Violation of Universal Lower Bound for the Shear Viscosity to Entropy Density Ratio in Dark Energy Dominated Accretion
• Equilibration and hydrodynamics at strong and weak coupling
• Two theorems for the gradient expansion of relativistic hydrodynamics
• Second order transport coefficients of nonconformal relativistic fluids in various dimensions from Dp-brane
• Higher-Curvature Gravity, Black Holes and Holography
• Holographic Constraints on Generalised Rivlin-Ericksen Fluid
• Graviton multi-point amplitudes for higher-derivative gravity in anti-de Sitter space
• Time evolving fluid from Vaidya spacetime