Fast scrambling in holographic Einstein-Podolsky-Rosen pair

Abstract

We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair exhibits fast scrambling. Strongly entangled quark and antiquark in $\mathcal{N}=4$ super Yang-Mills theory are considered. Their gravity dual is a fundamental string whose endpoints are uniformly accelerated in opposite direction. We slightly increase the acceleration of the endpoint and show that it quickly destroys the correlation between the quark and antiquark. The proper time scale of the destruction is ${\tau }_{\ast }\sim \beta \ln S$ where $\beta$ is the inverse Unruh temperature and $S$ is the entropy of the accelerating quark. We also evaluate the Lyapunov exponent from correlation function as ${\lambda }_L=2\pi /\beta$, which saturates the Lyapunov bound. Our results suggest that the fast scrambling or saturation of the Lyapunov bound do not directly imply the existence of an Einstein dual. When we slightly decrease the acceleration, the quark and antiquark are causally connected and an "one-way traversable wormhole" is created on the worldsheet. It causes the divergence of the correlation function between the quark and antiquark.

arXiv comment18 pages, 6 figures

References in corpus (22)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Eternal Black Holes in AdS
• Black holes and the butterfly effect
• Towards a derivation of holographic entanglement entropy
• Cool horizons for entangled black holes
• Fast Scramblers
• Complexity Equals Action
• Localized shocks
• Multiple Shocks
• Two-dimensional conformal field theory and the butterfly effect
• Entanglement Tsunami: Universal Scaling in Holographic Thermalization
• Momentum fluctuations of heavy quarks in the gauge-string duality
• The holographic dual of an EPR pair has a wormhole
• Conformal Bootstrap, Universality and Gravitational Scattering
• On the exact solution of the accelerating string in $Ad{S}_5$ space
• Scrambling time from local perturbations of the eternal BTZ black hole
• Quantum Fluctuations and the Unruh Effect in Strongly-Coupled Conformal Field Theories
• Holographic EPR Pairs, Wormholes and Radiation
• Dynamical AdS strings across horizons

Cited by in corpus (15)

• Chaotic strings in AdS/CFT
• Thouless time for mass-deformed SYK
• Wormholes & Holography: An Introduction
• Real Time Dynamics in Low Point Correlators in 2d BCFT
• On the interplay between magnetic field and anisotropy in holographic QCD
• Delocalizing Entanglement of Anisotropic Black Branes
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Maximal Chaos from Strings, Branes and Schwarzian Action
• Chaos, Diffusivity, and Spreading of Entanglement in Magnetic Branes, and the Strengthening of the Internal Interaction
• Schwinger-Keldysh effective action for relativistic Brownian particle in AdS-CFT
• Quantum information probes of charge fractionalization in large-$N$ gauge theories
• Quantum Correction to Chaos in Schwarzian Theory
• Worldsheet traversable wormholes
• Holographic RG flow and reparametrization invariance of Wilson Loops
• Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair