High Energy Theory Seminar

In this presentation, we argue that conditional probability provides a unified framework for quantizing geometry from the operator algebraic perspective. To illustrate this point, we address the role of geometry in quantum gravity in a sequence of three levels of increasingly general analysis. At the first level, we recall the intimate connection between exact quantum error correction and the algebraic RT formula as facilitated by quantum conditional expectations. At the second level, we describe the construction of subregion algebras to leading order in gravitational perturbation theory by appealing to the crossed product construction. The first two levels of analysis result in forms of the generalized entropy in which the area is treated as a central and thus commutative operator. To obtain a fully non-commutative area operator, we must incorporate effects that are present at higher orders in perturbation theory. At the third level of analysis, we propose an algebraic approach to quantifying these effects by invoking a non-commutative form of Bayes' law. We conclude with some brief remarks about the non-perturbative regime in which we propose a new class of fully background independent quantum gravitational observables.

The talk is in 469 Lauritsen.

Contact theoryinfo@caltech.edu for Zoom information.