Type I von Neumann algebras from bulk path integrals: Understanding RT without invoking AdS/CFT

The Ryu-Takayanagi (RT) formula is usually understood as computing an entropy in a dual boundary CFT. I will present recent work showing that RT can also be understood purely in the bulk as computing an entropy on an algebra of bulk observables. In particular, I will show that any gravitational path integral satisfying a simple set of axioms defines such bulk algebras. They are type I von Neumann algebras whose centers must have discrete spectra. The gravitational path integral also defines entropies on these algebras. I will show an interesting quantization property that gives our entropies a standard state-counting interpretation. Furthermore, in appropriate semiclassical limits our entropies are computed by the RT formula, thus providing a bulk Hilbert space interpretation of the RT entropy.