Journal Article

Generalized entropy for general subregions in quantum gravity

Speranza, Antony J., Jensen, Kristan, Sorce, Jonathan

2023

Overview

A bstract We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the G N → 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.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: Algebra / Classical and Quantum Gravitation / Elementary Particles / Entropy / Gauge Symmetry / Hamiltonian functions / High energy physics / Models of Quantum Gravity / Operators (mathematics) / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum gravity / Quantum Physics / Regular Article - Theoretical Physics / Relativity Theory / Renormalization and Regularization / String Theory