Thermal Noise and Stochastic Strings in AdS/CFT

Abstract

We clarify the structure of thermal noise in AdS/CFT by studying the dynamics of an equilibrated heavy quark string. Using the Kruskal extension of the correspondence to generate the dynamics of the field theory on the Keldysh contour, we show that the motion of the string is described by the classical equations of motion with a stochastic boundary condition on the stretched horizon. The form of the stochastic boundary condition is consistent with the dissipation on this surface and is found by integrating out the fluctuations inside of the stretched horizon. Solving the equations of motion for the fluctuating string we determine the full frequency dependence of the random force on the boundary quark and show that it is consistent with the frequency dependent dissipation. We show further that the stochastic motion reproduces the bulk to bulk two point functions of the Kruskal formalism. These turn out to be related to the usual retarded bulk to bulk propagator by KMS relations. Finally we analyze the stochastic equations and give a bulk picture of the random boundary force as a flip-flopping trailing string solution. The basic formalism can be applied to the fluctuations of gravitons, dilatons, and other fields.

29 Pages and six figures, typos fixed, references added

References in corpus (37)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• From AdS/CFT correspondence to hydrodynamics
• Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
• The Effect of Shear Viscosity on Spectra, Elliptic Flow, and HBT Radii
• Drag force in AdS/CFT
• Holography and hydrodynamics: diffusion on stretched horizons
• Universality of the shear viscosity in supergravity
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Heavy Quark Diffusion in Strongly Coupled $\mathbb{N}=4$ Yang Mills
• Wilson-Polyakov Loop at Finite Temperature in Large N Gauge Theory and Anti-de Sitter Supergravity
• Simulating elliptic flow with viscous hydrodynamics
• Suppression of elliptic flow in a minimally viscous quark-gluon plasma
• Saturation of Elliptic Flow and the Transport Opacity of the Gluon Plasma at RHIC
• An AdS/CFT Calculation of Screening in a Hot Wind
• Momentum fluctuations of heavy quarks in the gauge-string duality
• Transverse Momentum Broadening of a Fast Quark in a $\mathbb{N}=4$ Yang Mills Plasma
• Holographic melting and related properties of mesons in a quark gluon plasma
• An Action for Black Hole Membranes
• On universality of stress-energy tensor correlation functions in supergravity
• Holographic spectral functions and diffusion constants for fundamental matter
• The Energy of a Moving Quark-Antiquark Pair in an N=4 SYM Plasma
• Hydrodynamic Fluctuations, Long-time Tails, and Supersymmetry
• On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
• Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order
• The stress-energy tensor of a quark moving through a strongly-coupled N=4 supersymmetric Yang-Mills plasma: comparing hydrodynamics and AdS/CFT
• Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes
• Jets in strongly-coupled N = 4 super Yang-Mills theory
• Dissipative effects from transport and viscous hydrodynamics
• Black Hole Evaporation along Macroscopic Strings
• Particle abundance in a thermal plasma: quantum kinetics vs. Boltzmann equation
• Stochastic treatment of Disoriented Chiral Condensates within a Langevin description
• Quarkonium transport in thermal AdS/CFT

Cited by in corpus (82)

• Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions
• QCD and strongly coupled gauge theories: challenges and perspectives
• Heavy ions and string theory
• Improved Holographic QCD
• A holographic view on physics out of equilibrium
• Thermal Transport and Drag Force in Improved Holographic QCD
• Universal far-from-equilibrium Dynamics of a Holographic Superconductor
• Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT
• The Fluid Manifesto: Emergent symmetries, hydrodynamics, and black holes
• Horizon constraints on holographic Green's functions
• Chaotic strings in AdS/CFT
• Open quantum systems and Schwinger-Keldysh holograms
• Hawking Radiation and Non-equilibrium Quantum Critical Current Noise
• Langevin diffusion of heavy quarks in non-conformal holographic backgrounds
• Hydrodynamic Long-Time tails From Anti de Sitter Space
• Fluctuation, dissipation, and thermalization in non-equilibrium AdS_5 black hole geometries
• Real-time quantum dynamics of heavy quark systems at high temperature
• Universal Properties of the Langevin Diffusion Coefficients
• Heavy Quark Diffusion in Strongly Coupled Anisotropic Plasmas
• Quantum Fluctuations and the Unruh Effect in Strongly-Coupled Conformal Field Theories
• Quarkonium above deconfinement as an open quantum system
• Off-shell hydrodynamics from holography
• Holographic Quantum Quench
• Nonlinear Langevin dynamics via holography
• Lorentz violation, Gravity, Dissipation and Holography
• Fermionic pole-skipping in holography
• Holographic EPR Pairs, Wormholes and Radiation
• Holographic Brownian Motion and Time Scales in Strongly Coupled Plasmas
• Fluctuation and dissipation in de Sitter space
• A Tail of a Quark in N=4 SYM
• Fluctuation and Dissipation at a Quantum Critical Point
• Numerical integration of thermal noise in relativistic hydrodynamics
• Stochastic String Motion Above and Below the World Sheet Horizon
• Effective field theory of stochastic diffusion from gravity
• Brownian motion in strongly coupled, anisotropic Yang-Mills plasma: A holographic approach
• Fate of in-medium heavy quarks via a Lindblad equation
• Accelerated detectors and worldsheet horizons in AdS/CFT
• Early-Time Energy Loss in a Strongly-Coupled SYM Plasma
• All order effective action for charge diffusion from Schwinger-Keldysh holography
• Holographic Brownian Motion in Magnetic Environments
• Heavy quarks in a magnetic field
• Maximal Chaos from Strings, Branes and Schwarzian Action
• Schwinger Effect and Negative Differential Conductivity in Holographic Models
• Drag and jet quenching of heavy quarks in a strongly coupled N=2* plasma
• Ginzburg-Landau effective action for a fluctuating holographic superconductor
• The Gluonic Field of a Heavy Quark in Conformal Field Theories at Strong Coupling
• Schwinger-Keldysh effective action for relativistic Brownian particle in AdS-CFT
• Quantum Fluctuation and Dissipation in Holographic Theories: A Unifying Study Scheme
• Holographic Brownian Motion in Two Dimensional Rotating Fluid
• Open effective theory of scalar field in rotating plasma
• Holographic KMS relations at finite density
• Pointlike probes of superstring-theoretic superfluids
• Holographic Brownian motion at finite density
• Stochastic Equations in Black Hole Backgrounds and Non-equilibrium Fluctuation Theorems
• Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields
• Fluctuation and Dissipation from a Deformed String/Gauge Duality Model
• Quantum Decoherence with Holography
• Mobile impurity near the superfluid-Mott insulator quantum critical point in two dimensions
• Holographic Approach to Nonequilibrium Dynamics of Moving Mirrors Coupled to Quantum Critical Theories
• 4-point correlators in finite-temperature AdS/CFT: jet quenching correlations
• Out of time ordered effective dynamics of a quartic oscillator
• Holographic Schwinger-Keldysh field theory of SU(2) diffusion
• Holographic influence functional and its application to decoherence induced by quantum critical theories
• String in AdS Black Hole: A Thermo Field Dynamic Approach
• A path integral approach to the Langevin equation
• Fermionic Schwinger-Keldysh Propagators from AdS/CFT
• The confining trailing string
• Effective Mass of Holographic Brownian Particle in Rotating Plasma
• Dynamics of Heavy Quarks in Strongly Coupled $\mathcal{N}=4$ SYM Plasma
• A Holographic Description of Negative Energy States
• Subvacuum effects in Quantum Critical Theories from Holographic Approach
• QNM orthogonality relations for AdS black holes
• Gradient Correction to Photon Emission Rate at Strong Coupling
• Time dependent field correlators from holographic EPR pairs
• Zero Temperature Dissipation and Holography
• Environment-induced uncertainties on moving mirrors in quantum critical theories via holography
• Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach
• QCD, with Strings Attached
• Conformal Transformations and Strings for an Accelerating Quark-Antiquark Pair in AdS3
• Dissipative effects on quarkonium spectral functions
• Langevin Diffusion Coefficients Ratio in STU Model with Higher Derivative Corrections
• Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair