TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.5.134
TI  - 3d gravity from Virasoro TQFT: Holography, wormholes and knots
PY  - 2024/11/14
UR  - https://scipost.org/SciPostPhys.17.5.134
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 5
SP  - 134
A1  - Collier, Scott
AU  - Eberhardt, Lorenz
AU  - Zhang, Mengyang
AB  - We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper [SciPost Phys. 15, 151 (2023)]. We compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions. This matching is highly non-trivial, but can be checked directly in some examples. We then showcase the formalism in action, by computing the gravity partition functions of many relevant topologies. For holographic applications, we focus on the partition functions of Euclidean multi-boundary wormholes with three-punctured spheres as boundaries. This precisely quantifies the higher moments of the structure constants in the proposed ensemble boundary dual and subjects the proposal to thorough checks. Finally, we investigate in detail the example of the figure eight knot complement as a hyperbolic 3-manifold. We show that the Virasoro TQFT partition function is identical to the partition function computed in Teichmüller theory, thus giving strong evidence for the equivalence of these TQFTs. We also show how to produce a large class of manifolds via Dehn surgery on the figure eight knot.
ER  -

@Article{10.21468/SciPostPhys.17.5.134,
	title={{3d gravity from Virasoro TQFT: Holography, wormholes and knots}},
	author={Scott Collier and Lorenz Eberhardt and Mengyang Zhang},
	journal={SciPost Phys.},
	volume={17},
	pages={134},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.5.134},
	url={https://scipost.org/10.21468/SciPostPhys.17.5.134},
}