Stochastic trailing string and Langevin dynamics from AdS/CFT

Abstract

Using the gauge/string duality, we derive a set of Langevin equations describing the dynamics of a relativistic heavy quark moving with constant average speed through the strongly-coupled N=4 SYM plasma at finite temperature. We show that the stochasticity arises at the string world-sheet horizon, and thus is causally disconnected from the black hole horizon in the space-time metric. This hints at the non-thermal nature of the fluctuations, as further supported by the fact that the noise term and the drag force in the Langevin equations do not obey the Einstein relation. We propose a physical picture for the dynamics of the heavy quark in which dissipation and fluctuations are interpreted as medium-induced radiation and the associated quantum-mechanical fluctuations. This picture provides the right parametric estimates for the drag force and the (longitudinal and transverse) momentum broadening coefficients.

25 pages, 4 figures

References in corpus (10)

• Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
• Drag force in AdS/CFT
• Viscosity, Black Holes, and Quantum Field Theory
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Heavy Quark Diffusion in Strongly Coupled $\mathbb{N}=4$ Yang Mills
• Momentum fluctuations of heavy quarks in the gauge-string duality
• Comparing energy loss and $p_{\perp }$-broadening in perturbative QCD with strong coupling $\mathcal{N}=4$ SYM theory
• Deep inelastic scattering off a N=4 SYM plasma at strong coupling
• On the exact solution of the accelerating string in $Ad{S}_5$ space
• Temperature versus acceleration: the Unruh effect for holographic models

Cited by in corpus (10)

• Improved Holographic QCD
• Langevin diffusion of heavy quarks in non-conformal holographic backgrounds
• Fluctuation and dissipation in de Sitter space
• A semi-holographic model for heavy-ion collisions
• Accelerated detectors and worldsheet horizons in AdS/CFT
• Holographic Brownian Motion in Magnetic Environments
• Drag and jet quenching of heavy quarks in a strongly coupled N=2* plasma
• Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields
• Holographic influence functional and its application to decoherence induced by quantum critical theories
• Fermionic Schwinger-Keldysh Propagators from AdS/CFT