Open-closed 3d gravity as a random ensemble

TL;DR

This paper explores an ensemble of boundary conformal field theories within a tensor model framework to model 3d quantum gravity, introducing open-closed extensions and new predictions for manifolds with boundaries.

Contribution

It develops an open-closed extension of Virasoro TQFT in tensor models, connecting boundary CFTs with 3d gravity and proposing a purely open tensor model for bootstrap analysis.

Findings

Open-closed Virasoro TQFT extension derived

Predictions for off-shell bordered manifolds like annulus wormholes

Construction of a purely open tensor model for bootstrap studies

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.