Chaos and pole skipping in CFT${}_2$

Abstract

Recent work has suggested an intriguing relation between quantum chaos and energy density correlations, known as pole skipping. We investigate this relationship in two dimensional conformal field theories on a finite size spatial circle by studying the thermal energy density retarded two-point function on a torus. We find that the location ${\omega }_{\ast }=i\lambda$ of pole skipping in the complex frequency plane is determined by the central charge and the stress energy one-point function $⟨T⟩$ on the torus. In addition, we find a bound on $\lambda$ in $c>1$ compact, unitary CFT${}_2$s identical to the chaos bound, $\lambda \le 2\pi T$. This bound is saturated in large $c$ CFT${}_2$s with a sparse light spectrum, as quantified by arXiv:1405.5137, for all temperatures above the dual Hawking-Page transition temperature.

arXiv comment16 pages, 2 figures

References in corpus (49)

• A bound on chaos
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Holography from Conformal Field Theory
• Localized shocks
• Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes
• Two-dimensional conformal field theory and the butterfly effect
• An Apologia for Firewalls
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Emergent Spacetime and Holographic CFTs
• Causality Constraints in Conformal Field Theory
• A quantum hydrodynamical description for scrambling and many-body chaos
• Black hole scrambling from hydrodynamics
• Many-body chaos and energy dynamics in holography
• Bounding the Space of Holographic CFTs with Chaos
• The complex life of hydrodynamic modes
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Effective Field Theory for Chaotic CFTs
• Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
• On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
• Horizon constraints on holographic Green's functions
• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping
• String Universality for Permutation Orbifolds
• Phase transitions in symmetric orbifold CFTs and universality
• Bounds on transport from univalence and pole-skipping
• Chaos in the butterfly cone
• Permutation orbifolds and holography
• Transport and chaos in lattice Sachdev-Ye-Kitaev models
• Quasinormal modes in charged fluids at complex momentum
• Pole-skipping with finite-coupling corrections
• Quantum Chaos in Topologically Massive Gravity
• Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
• Classifying pole-skipping points
• On systems of maximal quantum chaos
• Fermionic pole-skipping in holography
• Real Time Dynamics in Low Point Correlators in 2d BCFT
• Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography
• Holographic chaos, pole-skipping, and regularity
• Pole-skipping and Rarita-Schwinger fields
• Pole-skipping and zero temperature
• Higher curvature corrections to pole-skipping
• Constraints on quasinormal modes and bounds for critical points from pole-skipping
• Quantum chaos, pole-skipping and hydrodynamics in a holographic system with chiral anomaly
• Permutation Orbifolds and Chaos
• Notes on Scrambling in Conformal Field Theory
• Scrambling in Two-Dimensional Conformal Field Theories with Light and Smeared Operators

Cited by in corpus (7)

• Pole-skipping and Rarita-Schwinger fields
• Quasi-normal modes of dyonic black holes and magneto-hydrodynamics
• Subleading Bounds on Chaos
• Construction of bulk solutions for towers of pole-skipping points
• Extremal Chaos
• Scrambling with conservation law
• Quantum information scrambling and quantum chaos in little string theory