Princeton University High Energy Theory Seminar

Abstract: I will describe recent progress towards understanding the gravitational path integral in AdS_3 quantum gravity and its boundary interpretation. A central question is: which spacetime topologies should be included in the path integral, and why? To address this question, we formulate a "statistical bootstrap" that constrains the universal statistics of heavy OPE data in the boundary theory, imposing crossing symmetry and "typicality" (a generalization of the eigenstate thermalization hypothesis). These constraints are geometrized by surgery moves on bulk manifolds that we call the "gravitational machine," leading to an infinite set of non-handlebody topologies that we argue must be included in the path integral. The machine generates only on-shell (hyperbolic) manifolds, whose partition functions can be computed exactly using Virasoro TQFT. But not all hyperbolic manifolds are produced. This reveals a large landscape of consistent sums over topologies. Based on joint work with Alexandre Belin, Lorenz Eberhardt, Diego Liska, and Boris Post.