Open-closed 3d gravity as a random ensemble

TL;DR

We develop a BCFT-driven quantum gravity framework by embedding BCFT data into a tensor-matrix model and obtaining an open-closed extension of Virasoro TQFT whose bulk limit includes tensionful end-of-the-world branes. The construction squares six BCFT bootstrap constraints to form a tensor potential $V_1$–$V_6$ and couples torus/annulus modular data into a matrix potential, defining a topological expansion over 3-manifolds with bordered boundaries. We provide a detailed 3d interpretation mapping $(C,B,D,A)$ data to bulk/boundary Wilson lines, derive propagators and interaction vertices, and demonstrate that the model realizes an open-closed Virasoro TQFT with predictions for off-shell geometries such as the annulus wormhole. The work also develops a purely open bootstrap, extends to non-orientable BCFTs, and proposes a brane action that mirrors the surgery-based gluing, illustrating an ensemble perspective on BCFT holography and 3d gravity with EOW branes.

Abstract

We investigate an ensemble of boundary CFTs within the framework of a tensor model recently constructed to model 3d quantum gravity. The incorporation of CFT borders introduces new elements to the gravity theory. In particular, it leads to an open-closed extension of Virasoro TQFT, which in the classical limit gives rise to 3d gravity with tensionful end-of-the-world branes. It also provides predictions for off-shell manifolds with bordered asymptotic boundaries, such as the annulus wormhole. As an application, we construct a purely open variant of the tensor model to study a purely open bootstrap problem in the context of CFT triangulation. We also briefly discuss the extension to non-orientable CFTs.