von Neumann algebras in JT gravity

Abstract

We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II${}_{\infty }$ factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit. We comment on how the factorization problem differs between pure JT gravity and JT gravity with matter.

arXiv comment35 pages + appendices. v2: typos fixed, appendix added

References in corpus (23)

• Comments on the Sachdev-Ye-Kitaev model
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Fermionic Localization of the Schwarzian Theory
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Local subsystems in gauge theory and gravity
• Local bulk operators in AdS/CFT: a boundary view of horizons and locality
• An Algebra of Observables for de Sitter Space
• Solving the Schwarzian via the Conformal Bootstrap
• Gravity and the Crossed Product
• The Quantum Gravity Dynamics of Near Extremal Black Holes
• Towards a full solution of the large N double-scaled SYK model
• Entanglement entropy and nonabelian gauge symmetry
• Large N algebras and generalized entropy
• The bulk Hilbert space of double scaled SYK
• Statistical mechanics of a two-dimensional black hole
• Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction
• Defects in Jackiw-Teitelboim Quantum Gravity
• Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK
• Symmetries Near the Horizon
• Fine Structure of Jackiw-Teitelboim Quantum Gravity
• Looking at supersymmetric black holes for a very long time
• An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity
• Dynamics of black holes in Jackiw-Teitelboim gravity

Cited by in corpus (18)

• Generalized entropy for general subregions in quantum gravity
• A symmetry algebra in double-scaled SYK
• Crossed product algebras and generalized entropy for subregions
• Generalized Black Hole Entropy is von Neumann Entropy
• Quantum Null Geometry and Gravity
• A Type $I$ Approximation of the Crossed Product
• Hartle-Hawking state and its factorization in 3d gravity
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Multiway Junction Conditions: Booklets and Webs
• Black hole complementarity from microstate models: A study of information replication and the encoding in the black hole interior
• On the Nonequilibrium Dynamics of Gravitational Algebras
• Extremality as a Consistency Condition on Subregion Duality
• Discrete JT gravity as an Ising model
• Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity
• Linearization (in)stabilities and crossed products
• Gravitational algebras and applications to nonequilibrium physics
• Fiducial observers and the thermal atmosphere in the black hole quantum throat