Type I von Neumann algebras from gravitational path integrals: Ryu–Takayanagi as entropy without holography

APA

Colafranceschi, E. (2024). Type I von Neumann algebras from gravitational path integrals: Ryu–Takayanagi as entropy without holography. Perimeter Institute for Theoretical Physics. https://pirsa.org/24040078

MLA

Colafranceschi, Eugenia. Type I von Neumann algebras from gravitational path integrals: Ryu–Takayanagi as entropy without holography. Perimeter Institute for Theoretical Physics, Apr. 04, 2024, https://pirsa.org/24040078

BibTex

          @misc{ scivideos_PIRSA:24040078,
            doi = {10.48660/24040078},
            url = {https://pirsa.org/24040078},
            author = {Colafranceschi, Eugenia},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Type I von Neumann algebras from gravitational path integrals: Ryu{\textendash}Takayanagi as entropy without holography},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {apr},
            note = {PIRSA:24040078 see, \url{https://scivideos.org/pirsa/24040078}}
          }
          

Eugenia Colafranceschi University of California, Santa Barbara

Source RepositoryPIRSA
Collection

Abstract

We show that the Ryu-Takayanagi (RT) formula, originally introduced to compute the entropy of a holographic boundary CFT, can be interpreted as entropy of an algebra of bulk gravitational observables. In particular, we show that any Euclidean gravitational path integral satisfying a simple and familiar set of axioms defines type I von Neumann algebras of bulk observables acting on closed codimension-2 asymptotic boundaries. The entropies associated to these algebras, defined via the gravitational path integral, can be written in terms of standard density matrices and standard Hilbert space traces, and in appropriate semiclassical limits are computed by the RT formula with quantum corrections. Our work thus provides a bulk state-counting interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, they may be expected to hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

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