Von Neumann algebras in JT gravity

DOI10.1007/JHEP06(2023)067arXiv2303.04701OpenAlexW4380681741MaRDI QIDQ6176347

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Publication date: 25 July 2023

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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${}_{i}nfty$ 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.

Full work available at URL: https://arxiv.org/abs/2303.04701

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