基于赛弗特纤维化算子的3D-3D对应
3D-3D Correspondence from Seifert Fibering Operators
AI总结：
该研究利用赛弗特纤维化算子构建了与赛弗特流形对偶的TQFT态积分模型必要成分，展示了湮灭双曲三维流形上TQFT波函数的差分算子，为底层TQFT结构提供线索。
摘要：
利用近期为3D $\mathcal{N} = 2$ 规范理论开发的赛弗特纤维化算子，我们构建了拓扑量子场论（TQFT）态积分模型的必要成分，该模型在3D-3D对应下与给定赛弗特流形对偶，重点研究具有正轨形欧拉特征的赛弗特同调球情形。我们进一步展示了一组差分算子，它们在双曲三维流形上湮灭该TQFT的波函数，推广了透镜空间配分函数和全纯块的类似构造。这些性质为揭示底层TQFT的结构提供了有趣线索。
英文摘要：
Using recently developed Seifert fibering operators for 3D $\mathcal{N} = 2$ gauge theories, we formulate the necessary ingredients for a state-integral model of the topological quantum field theory dual to a given Seifert manifold under the 3D-3D correspondence, focusing on the case of Seifert homology spheres with positive orbifold Euler characteristic. We further exhibit a set of difference operators that annihilate the wavefunctions of this TQFT on hyperbolic three-manifolds, generalizing similar constructions for lens space partition functions and holomorphic blocks. These properties offer intriguing clues as to the structure of the underlying TQFT.
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