July 31, 2023 to August 4, 2023
Perimeter Institute for Theoretical Physics
America/Toronto timezone

Talk 88 - Type II_1 algebras for local subregions in quantum gravity

Jul 31, 2023, 10:00 AM
PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)

PI/1-100 - Theatre

Perimeter Institute for Theoretical Physics



Antony Speranza (University of Illinois, Urbana-Champaign)


We argue that generic local subregions in semiclassical quantum gravity are associated with von Neumann algebras of type II_1, extending recent work by Chandrasekaran et.al. beyond subregions bounded by Killing horizons. The subregion algebra arises as a crossed product of the type III_1 algebra of quantum fields in the subregion by the flow generated by a gravitational constraint operator. We conjecture that this flow agrees with the vacuum modular flow sufficiently well to conclude that the resulting algebra is type II_\infty, which projects to a type II_1 algebra after imposing a positive energy condition. The entropy of semiclassical states on this algebra can be computed and shown to agree with the generalized entropy by appealing to a first law of local subregions. The existence of a maximal entropy state for the type II_1 algebra is further shown to imply a version of Jacobson’s entanglement equilibrium hypothesis. We discuss other applications of this construction to quantum gravity and holography, including the quantum extremal surface prescription and the quantum focusing conjecture.

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