Solving 3d gravity with Virasoro TQFT

Journal Article · Wed Oct 11 00:00:00 EDT 2023 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.15.4.151· OSTI ID:2008998

Collier, Scott ^[1]; Eberhardt, Lorenz ^[2]; Zhang, Mengyang ^[1]

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1. Princeton University
2. Institute for Advanced Study

We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as “Virasoro TQFT”. This TQFT is similar, but importantly not equivalent, to SL(2, \mathbb{R} $ℝ$ ) Chern-Simons theory. This sharpens the folklore that 3d gravity is related to SL(2, \mathbb{R} $ℝ$ ) Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0009988
• OSTI ID: 2008998
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 4 Vol. 15; ISSN 2542-4653
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English