Higher Derivative Corrections to Shear Viscosity from Graviton's Effective Coupling

Abstract

The shear viscosity coefficient of strongly coupled boundary gauge theory plasma depends on the horizon value of the effective coupling of transverse graviton moving in black hole background. The proof for the above statement is based on the canonical form of graviton's action. But in presence of generic higher derivative terms in the bulk Lagrangian the action is no longer canonical. We give a procedure to find an effective action for graviton (to first order in coefficient of higher derivative term) in canonical form in presence of any arbitrary higher derivative terms in the bulk. From that effective action we find the effective coupling constant for transverse graviton which in general depends on the radial coordinate $r$. We also argue that horizon value of this effective coupling is related to the shear viscosity coefficient of the boundary fluid in higher derivative gravity. We explicitly check this procedure for two specific examples: (1) four derivative action and (2) eight derivative action ($Wey{l}^4$ term). For both cases we show that our results for shear viscosity coefficient (up to first order in coefficient of higher derivative term) completely agree with the existing results in the literature.

0 + 23 pages

References in corpus (45)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• 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
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• What RHIC Experiments and Theory tell us about Properties of Quark-Gluon Plasma ?
• Quasinormal modes and holography
• Holography and hydrodynamics: diffusion on stretched horizons
• Viscosity Bound Violation in Higher Derivative Gravity
• Viscosity, Black Holes, and Quantum Field Theory
• Fluid dynamics of R-charged black holes
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Why does the Quark-Gluon Plasma at RHIC behave as a nearly ideal fluid ?
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Coupling Constant Dependence in the Thermodynamics of N=4 Supersymmetric Yang-Mills Theory
• From AdS/CFT correspondence to hydrodynamics. II. Sound waves
• Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang-Mills theory
• Asymptotic perfect fluid dynamics as a consequence of AdS/CFT
• Beyond eta/s = 1/4pi
• Entropy Current in Conformal Hydrodynamics
• Gauge/gravity duality and thermalization of a boost-invariant perfect fluid
• Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality
• Quantum corrections to eta/s
• Shear Viscosity from Effective Couplings of Gravitons
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• The Hydrodynamics of M-Theory
• Resolving disagreement for eta/s in a CFT plasma at finite coupling
• Universal holographic hydrodynamics at finite coupling
• Shear Viscosity from Gauss-Bonnet Gravity with a Dilaton Coupling
• Expanding plasmas and quasinormal modes of anti-de Sitter black holes
• Forced Fluid Dynamics from Gravity
• Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT
• Black Hole Dynamics From Atmospheric Science
• The Sound of M-Theory
• Shear viscosity of boost invariant plasma at finite coupling
• The ratio of shear viscosity to entropy density in generalized theories of gravity
• On Euclidean and Noetherian Entropies in AdS Space
• Second order hydrodynamics of a CFT plasma from boost invariant expansion
• Consistent holographic description of boost-invariant plasma
• Higher Derivative Corrections to Locally Black Brane Metrics
• Strongly Coupled Quark-Gluon Plasma: The Status Report
• Linearized hydrodynamics from probe-sources in the gauge-string duality
• The shear diffusion coefficient for generalized theories of gravity
• On the universal hydrodynamics of strongly coupled CFTs with gravity duals

Cited by in corpus (35)

• Quasinormal modes of black holes and black branes
• Holographic studies of quasi-topological gravity
• Holographic Hydrodynamics with a Chemical Potential
• Black Holes in (Quartic) Quasitopological Gravity
• On Charged Lifshitz Black Holes
• Transport coefficients, membrane couplings and universality at extremality
• Holography of Charged Dilaton Black Holes in General Dimensions
• Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity
• The Quantum Viscosity Bound In Lovelock Gravity
• Near-Horizon Analysis of $\eta /s$
• Generating Temperature Flow for eta/s with Higher Derivatives: From Lifshitz to AdS
• Universality of second order transport in Gauss-Bonnet gravity
• Anti de Sitter black holes and branes in dynamical Chern-Simons gravity: perturbations, stability and the hydrodynamic modes
• R^2 Corrections to Asymptotically Lifshitz Spacetimes
• The universal viscosity to entropy density ratio from entanglement
• Transport Coefficients from Extremal Gauss-Bonnet Black Holes
• Moduli and electromagnetic black brane holography
• Near horizon data and physical charges of extremal AdS black holes
• Equivalence of JT Gravity and Near-extremal Black Hole Dynamics in Higher Derivative Theory
• Viscosity bound for anisotropic superfluids in higher derivative gravity
• Proof of a universal lower bound on the shear viscosity to entropy density ratio
• Nonlinear Hydrodynamics from Flow of Retarded Green's Function
• $Ad{S}_5$ black hole at N=2 supergravity
• $\eta /s$ at finite coupling
• Hydrodynamics in black brane with hyperscaling violation metric background
• The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant
• Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual
• Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity
• Stringy effects in black hole decay
• On Classical Equivalence Between Noncritical and Einstein Gravity : The AdS/CFT Perspectives
• The Weak Gravity Conjecture and the Viscosity Bound with Six-Derivative Corrections
• Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma
• The correlation of WGC and Hydrodynamics bound with $R^4$ correction in the charged AdS${}_{d+2}$ black brane
• Hall viscosity to entropy ratio in higher derivative theories
• Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation