Generalized entropy for general subregions in quantum gravity
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13130_2023_Article_22330.pdf
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Author(s)
Jensen, Kristan
Sorce, Jonathan
Speranza, Antony J.
Date Issued
December 4, 2023
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2023 Dec 04;2023(12):20
Version
Final published version
Abstract
We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the GN → 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 II1, 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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP12(2023)020
