Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect

Abstract

We study the theory of Jackiw-Teitelboim gravity with generalized dilaton potential on Euclidean two-dimensional negatively curved backgrounds. The effect of the generalized dilaton potential is to induce a conical defect on the two-dimensional manifold. We show that this theory can be written as the ordinary quantum mechanics of a charged particle on a hyperbolic disk in the presence of a constant background magnetic field plus a pure gauge Aharonov-Bohm field. This picture allows us to exactly calculate the wavefunctions and propagators of the corresponding gravitational dynamics. With this method we are able to reproduce the gravitational density of states as well as compute the Réyni and entanglement entropies for the Hartle-Hawking state. While we reproduce the classical entropy at high temperature, we also find an extra topological contribution that becomes dominant at low temperatures. We then show how the presence of defects modify correlation functions, including the out-of-time-ordered correlation, and decrease the Lyapunov exponent. This is achieved two ways: by directly quantizing the boundary Schwarzian theory and by dimensionally reducing $SL(2,\mathbb{Z})$ black holes.

arXiv comment64 pages, 2 figures

References in corpus (52)

• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Generalized gravitational entropy
• Building up spacetime with quantum entanglement
• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• Holographic Entanglement Entropy: An Overview
• The Page curve of Hawking radiation from semiclassical geometry
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• An Investigation of AdS${}_2$ Backreaction and Holography
• Quantum Gravity Partition Functions in Three Dimensions
• The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
• Delta M_K and epsilon_K in SUSY at the Next-to-Leading order
• Fermionic Localization of the Schwarzian Theory
• Diving into traversable wormholes
• Holographic Entanglement Entropy
• Holographic Mutual Information is Monogamous
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Solving the Schwarzian via the Conformal Bootstrap
• JT gravity as a matrix integral
• Bi-Local Holography in the SYK Model
• The Holographic Entropy Cone
• The Quantum Gravity Dynamics of Near Extremal Black Holes
• On the Dynamics of Near-Extremal Black Holes
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
• The Schwarzian Theory - Origins
• Statistical mechanics of a two-dimensional black hole
• Low-dimensional de Sitter quantum gravity
• The Schwarzian Theory - A Wilson Line Perspective
• A universal Schwarzian sector in two-dimensional conformal field theories
• Defects in Jackiw-Teitelboim Quantum Gravity
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Schwinger pair production in AdS2
• AdS${}_2$/CFT${}_1$ correspondence and near-extremal black hole entropy
• Leading order corrections to the quantum extremal surface prescription
• Bekenstein-Hawking Entropy as Topological Entanglement Entropy
• Trouble For Remnants
• On the Chaos Bound in Rotating Black Holes
• Gauge Theories for Gravity on a Line
• Finite-cutoff JT gravity and self-avoiding loops
• Deformations of the Almheiri-Polchinski model
• SYK Correlators for All Energies
• Entanglement entropy in Jackiw-Teitelboim Gravity
• Aharonov-Bohm effect on the Poincaré disk
• Hyperbolic geometrical optics: Hyperbolic glass

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• Gravity without averaging
• Generalized Jackiw-Teitelboim gravity in presence of Bloch brane-like models
• Pacman geometries and the Hayward term in JT gravity
• Classical geometry from the tensionless string
• Bulk-boundary entanglement correspondence and the Ryu-Takayanagi conjecture in an $Ad{S}_2/CF{T}_1$ setup
• Aspects of Jackiw-Teitelboim Gravity in Anti-de Sitter and de Sitter spacetime