近日，美国斯坦福大学Yan, Cynthia团队研究了通过VTQFT解决三维壳几何谜题。这一研究成果发表在2025年9月11日出版的《高能物理杂志》上。

研究组指出，将Virasoro TQFT方法简单应用于计算两种壳外三维几何的路径积分存在困难。Maxfield-Turiaci[1]提出通过对被称为Seifert流形的壳外几何求和来解决纯三维重力的负性问题。

研究组尝试计算以Virasoro TQFT为主题的Seifert流形。他们的结果并不完全符合Maxfield-Turiaci。研究组将差异归结为没有正确地包含映射类组。研究组还通过外推壳几何计算了一个三边界涡旋虫洞。他们遇到的挑战类似于在比较Cotler-Jensen[2]对涡旋虫洞的真正离壳计算和从壳上配置的外推中观察到的挑战。

附：英文原文

Title: Puzzles in 3D off-shell geometries via VTQFT

Author: Yan, Cynthia

Issue&Volume: 2025-09-11

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 [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.

DOI: 10.1007/JHEP09(2025)104

Source: https://link.springer.com/article/10.1007/JHEP09(2025)104