The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity

TL;DR

This paper explores a model of 3d gravity using open Virasoro TQFT, revealing how it computes gravitational path integrals with specific boundary conditions and connecting it to Conformal Turaev-Viro theory.

Contribution

It introduces a restricted open Virasoro TQFT for 3d gravity, demonstrating its role in calculating path integrals and establishing a duality with Conformal Turaev-Viro theory.

Findings

Computes gravitational path integrals with fixed-length and fixed-angle boundary conditions.

Shows the relation between Virasoro TQFT and Conformal Turaev-Viro theory via open-closed duality.

Identifies a class of manifolds involving boundary Wilson loops relevant to the model.

Abstract

We study a model of 3d gravity relevant to the open sector of a CFT ensemble. The quantum theory is the open Virasoro TQFT, obtained by restricting the full open-closed Virasoro TQFT to a subclass of admissible manifolds. We show that it computes gravitational path integrals on compact regions with fixed-length boundary conditions for states above the black hole threshold, and fixed-angle boundary conditions for states below the threshold. Focusing on a special class of manifolds involving only boundary Wilson loops, we further show that the relation between Conformal Turaev-Viro theory and the diagonal sector of two copies of Virasoro TQFT arises naturally from an open-closed duality.