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arXiv · 2502.16686

Puzzles in 3D Off-Shell Geometries via VTQFT

Cynthia Yan
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Abstract

We point out a difficulty with a naive application of Virasoro TQFT methods to compute path integrals for two types of off-shell 3-dimensional geometries. Maxfield-Turiaci proposed solving the negativity problem of pure 3d gravity by summing over off-shell geometries known as Seifert manifolds. We attempt to compute Seifert manifolds using Virasoro TQFT. Our results don't match completely with Maxfield-Turiaci. We trace the discrepancies to not including the mapping class group properly. We also compute a 3-boundary torus-wormhole by extrapolating from an on-shell geometry. We encounter challenges similar to those observed in the comparison between the genuine off-shell computation of a torus-wormhole by Cotler-Jensen and the extrapolation from an on-shell configuration.

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Cynthia Yan. 2026-01-13. Puzzles in 3D Off-Shell Geometries via VTQFT. https://arxiv.org/abs/2502.16686

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