Puzzles in 3D Off-Shell Geometries via VTQFT
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.
Cite
@article{arxiv.2502.16686,
title = {Puzzles in 3D Off-Shell Geometries via VTQFT},
author = {Cynthia Yan},
journal= {arXiv preprint arXiv:2502.16686},
year = {2026}
}
Comments
18 pages + appendices; minor corrections made, references added; references added