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

          @misc{ pirsa_PIRSA:23070005,
            doi = {10.48660/23070005},
            url = {https://pirsa.org/23070005},
            author = {Speranza, Antony},
            keywords = {Quantum Fields and Strings, Quantum Information, Quantum Foundations},
            language = {en},
            title = {Talk 88 - Type II_1 algebras for local subregions in quantum gravity},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {jul},
            note = {PIRSA:23070005 see, \url{https://pirsa.org}}
          }
          

Abstract

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.