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∞ 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.
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Acknowledgments
I thank Scott Collier, Daniel Harlow, Daniel Jafferis, Adam Levine, Hong Liu, Ronak Soni, Jon Sorce, and Gabriel Wong for stimulating discussions. I also thank Daniel Harlow and Jon Sorce for comments on the draft. This work is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under grant Contract Number DE-SC0012567 (High Energy Theory research) and the Department of Defense grant award KK2014.
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Kolchmeyer, D.K. von Neumann algebras in JT gravity. J. High Energ. Phys. 2023, 67 (2023). https://doi.org/10.1007/JHEP06(2023)067
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DOI: https://doi.org/10.1007/JHEP06(2023)067