PIRSA:24100122

Observables, Hilbert Spaces and Entropies from the Gravitational Path Integral

(2024). Observables, Hilbert Spaces and Entropies from the Gravitational Path Integral. Perimeter Institute. https://pirsa.org/24100122

Observables, Hilbert Spaces and Entropies from the Gravitational Path Integral. Perimeter Institute, Oct. 24, 2024, https://pirsa.org/24100122 

          @misc{ pirsa_PIRSA:24100122,
            doi = {10.48660/24100122},
            url = {https://pirsa.org/24100122},
            author = {},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Observables, Hilbert Spaces and Entropies from the Gravitational Path Integral},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {oct},
            note = {PIRSA:24100122 see, \url{https://pirsa.org}}
          }
Eugenia Colafranchesci
Talk number
PIRSA:24100122
Collection
Talk Type
Subject
Abstract

The Ryu-Takayanagi (RT) formula was originally introduced to compute the entropy of holographic boundary conformal field theories. In this talk, I will show how this formula can also be understood as the entropy of an algebra of bulk gravitational observables. Specifically, I will demonstrate that any Euclidean gravitational path integral, when it satisfies a simple set of properties, defines Hilbert spaces associated with closed codimension-2 asymptotic boundaries, along with type I von Neumann algebras of bulk observables acting on these spaces. I will further explain how the path integral naturally defines entropies on these algebras, and how an interesting quantization property leads to a standard state-counting interpretation. Finally, I will show that in the appropriate semiclassical limits, these entropies are computed via the RT formula, thereby providing a bulk Hilbert space interpretation of the RT entropy.