Generalized entropy for general subregions in quantum gravity

Abstract

We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\to 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we argue that the algebra is a type II von Neumann factor. To do so in the former case we introduce a model of an observer living in the region; in the latter, the ADM Hamiltonian effectively serves as an observer. In both cases the entropy of states on which this algebra acts is UV finite, and we find that it agrees, up to a state-independent constant, with the generalized entropy. For spatially compact regions the algebra is type II${}_1$, implying the existence of an entropy maximizing state, which realizes a version of Jacobson's entanglement equilibrium hypothesis. The construction relies on the existence of well-motivated but conjectural states whose modular flow is geometric at an instant in time. Our results generalize the recent work of Chandrasekaran, Longo, Penington, and Witten on an algebra of operators for the static patch of de Sitter space.

60 pages + 22 pages in appendices; v2 includes extra references and fixes some typos; v3 fixes two additional typos and matches the version in JHEP

References in corpus (8)

• Towards a derivation of holographic entanglement entropy
• Holographic representation of local bulk operators
• Setting the boundary free in AdS/CFT
• Relative entropy and the Bekenstein bound
• Observables, gravitational dressing, and obstructions to locality and subsystems
• Unitarity and Holography in Gravitational Physics
• Entanglement equilibrium for higher order gravity
• A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories

Cited by in corpus (34)

• Crossed product algebras and generalized entropy for subregions
• Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
• Generalized Black Hole Entropy is von Neumann Entropy
• Quantum Null Geometry and Gravity
• One-shot holography
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• A Type $I$ Approximation of the Crossed Product
• Geometric relational framework for general-relativistic gauge field theories
• A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC
• Semifinite von Neumann algebras in gauge theory and gravity
• Algebras and Hilbert spaces from gravitational path integrals: Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT
• Holographic Tensor Networks with Bulk Gauge Symmetries
• Gravitational entropy is observer-dependent
• Soft edges: the many links between soft and edge modes
• Modular Hamiltonian for de Sitter diamonds
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Generalised second law beyond the semiclassical regime
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• One-loop partition function of gravity with leaky boundary conditions
• Modular Fluctuations in Cosmology
• On the Nonequilibrium Dynamics of Gravitational Algebras
• Fluctuation theorems, quantum channels and gravitational algebras
• From spacetime thermodynamics to Weyl transverse gravity
• Squashed Entanglement from Generalized Rindler Wedge
• De Sitter Horizon Edge Partition Functions
• Extremality as a Consistency Condition on Subregion Duality
• Gravitational algebras and applications to nonequilibrium physics
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• Linearization (in)stabilities and crossed products
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Effective density matrix for vacua in asymptotically flat gravity
• Mechanics as a general-relativistic gauge field theory, and Relational Quantization
• Spectral Projections for Density Matrices in Quantum Field Theories
• Fiducial observers and the thermal atmosphere in the black hole quantum throat