Observables, Hilbert Spaces and Entropies from the Gravitational Path IntegralConfirmed

by Eugenia Colafranchesci (Western University)

Thursday Oct 24, 2024, 2:30 p.m. → 4:00 p.m. America/Toronto

PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)

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.