Analysis reveals discrepancies in path integrals for off-shell geometries, suggesting careful treatment of the mapping class group.
A bstract 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.
No takes yet. Share an insight, caveat, or question.
Cynthia Yan (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: