Generalized entropy for general subregions in quantum gravity

Author:

Jensen Kristan,Sorce JonathanORCID,Speranza Antony J.ORCID

Abstract

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.

Publisher

Springer Science and Business Media LLC

Subject

Nuclear and High Energy Physics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Null Raychaudhuri: canonical structure and the dressing time;Journal of High Energy Physics;2024-01-26

2. A type I approximation of the crossed product;Journal of High Energy Physics;2024-01-23

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