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<p>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 [1] 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 [2] and the extrapolation from an on-shell configuration.</p>

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Puzzles in 3D off-shell geometries via VTQFT

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  • 发表日期：

    2025年9月11日

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  • Cynthia Yan

摘要

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 [1] 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 [2] and the extrapolation from an on-shell configuration.