A universal Schwarzian sector in two-dimensional conformal field theories

Abstract

We show that an extremely generic class of two-dimensional conformal field theories (CFTs) contains a sector described by the Schwarzian theory. This applies to theories with no additional symmetries and large central charge, but does not require a holographic dual. Specifically, we use bootstrap methods to show that in the grand canonical ensemble, at low temperature with a chemical potential sourcing large angular momentum, the density of states and correlation functions are determined by the Schwarzian theory, up to parametrically small corrections. In particular, we compute out-of-time-order correlators in a controlled approximation. For holographic theories, these results have a gravitational interpretation in terms of large, near-extremal rotating BTZ black holes, which have a near horizon throat with nearly AdS${}_2\times S^1$ geometry. The Schwarzian describes strongly coupled gravitational dynamics in the throat, which can be reduced to Jackiw-Teitelboim (JT) gravity interacting with a $U(1)$ field associated to transverse rotations, coupled to matter. We match the physics in the throat to observables at the AdS${}_3$ boundary, reproducing the CFT results.

54 pp, 5 figs; v2 refs added

References in corpus (11)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• More on Supersymmetric and 2d Analogs of the SYK Model
• Higher Dimensional Generalizations of the SYK Model
• An exact quantization of Jackiw-Teitelboim gravity
• Lightcone Modular Bootstrap and Pure Gravity
• Defects in Jackiw-Teitelboim Quantum Gravity
• Jackiw-Teitelboim Gravity and Rotating Black Holes
• Chaos in the butterfly cone
• Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
• Dynamics of black holes in Jackiw-Teitelboim gravity

Cited by in corpus (62)

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• Liouville quantum gravity -- holography, JT and matrices
• Universal Dynamics of Heavy Operators in CFT${}_2$
• Random Matrix Theory for Complexity Growth and Black Hole Interiors
• Explorations of Non-Perturbative JT Gravity and Supergravity
• The Virasoro Minimal String
• Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes
• A proposal for 3d quantum gravity and its bulk factorization
• Beurling-Selberg Extremization and Modular Bootstrap at High Energies
• Aspects of AdS${}_2$ Quantum Gravity and the Karch-Randall Braneworld
• High Energy Modular Bootstrap, Global Symmetries and Defects
• AdS${}_3$ wormholes from a modular bootstrap
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• A JT supergravity as a double-cut matrix model
• Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects
• 3d gravity from Virasoro TQFT: Holography, wormholes and knots
• Averaging over moduli in deformed WZW models
• Gravitational perturbations from NHEK to Kerr
• Rotating Black Holes in AdS, Extremality and Chaos
• JT Gravity Limit of Liouville CFT and Matrix Model
• Rotating 5D Black Holes: Interactions and deformations near extremality
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• From black holes to baby universes in CGHS gravity
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• A quantum mechanics for magnetic horizons
• Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect
• Near-Extremal Limits of Warped CFTs
• Tearing down spacetime with quantum disentanglement
• Quantum Cross-section of Near-extremal Black Holes
• Hartle-Hawking state and its factorization in 3d gravity
• Phase transitions for deformations of JT supergravity and matrix models
• Near-Extremal Limits of Warped Black Holes
• The Schwarzian sector of higher spin CFTs
• Near Conformal Perturbation Theory in SYK Type Models
• Fast Scrambling of mutual information in Kerr-AdS${}_{\text{5}}$
• Lightcone Modular Bootstrap and Tauberian Theory: A Cardy-like Formula for Near-extremal Black Holes
• Black hole wavefunctions and microcanonical states
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Classical geometry from the tensionless string
• Gravitating spinning strings in AdS${}_3$
• Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
• Near-extremal dynamics away from the horizon
• Wigner meets 't Hooft near the black hole horizon
• Quantum Gravity Microstates from Fredholm Determinants
• Les Houches lectures on two-dimensional gravity and holography
• Boundary correlators and the Schwarzian mode
• Jackiw-Teitelboim gravity and near-extremal BTZ thermodynamics
• JT gravity and near-extremal thermodynamics for Kerr black holes in $Ad{S}_{4,5}$ for rotating perturbations
• Thermodynamic law and holography dual of accelerating and rotating black hole in Nariai limit
• Statistical Mechanics of Exponentially Many Low Lying States
• Universal sectors of two-dimensional Carrollian CFTs
• Higher spin wormholes from modular bootstrap
• Classical Unattainability of Extremality in non-BPS D-brane Systems
• Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity
• Four-point correlation modular bootstrap for OPE densities
• Aspects of Jackiw-Teitelboim Gravity in Anti-de Sitter and de Sitter spacetime
• The Fate of Nucleated Black Holes in de Sitter Quantum Gravity
• One-loop effect in the charged 2D black hole near extremality
• A universal sum over topologies in 3d gravity