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arXiv · 2604.09396

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

Daniel L. Jafferis·Diandian Wang
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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.

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Daniel L. Jafferis, Diandian Wang. 2026-04-10. The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity. https://arxiv.org/abs/2604.09396

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