## Video URL

https://pirsa.org/24100122# Observables, Hilbert Spaces and Entropies from the Gravitational Path Integral

### APA

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

### MLA

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

### BibTex

@misc{ scivideos_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 for Theoretical Physics}, year = {2024}, month = {oct}, note = {PIRSA:24100122 see, \url{https://scivideos.org/pirsa/24100122}} }

**Source Repository**PIRSA

**Collection**

**Talk Type**Scientific Series

## 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.