群流形上弦的定域化与阿贝尔化：非单连通情形
Localization and Abelianization of Strings on Group Manifolds: The Non-simply Connected Case
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中文总结 AI 辅助
该研究针对非单连通紧致连通单李群靶流形的WZW模型，推导了定域化公式，揭示了FGK上闭链、相对Rochlin不变量相关的拓扑效应，为其半经典定域化的拓扑贡献提供了统一描述。
中文摘要 AI 辅助
我们研究以非单连通紧致连通单李群流形为靶流形的Wess–Zumino–Witten（WZW）模型的配分函数。从Felder–Gawędzki–Kupiainen（FGK）的模不变配分函数出发，我们推导了一个定域化公式，该公式也可通过相应超对称WZW模型的超对称定域化直接得到。我们的结果揭示了与靶群非平凡拓扑相关的多种拓扑效应：Wess–Zumino振幅由FGK上闭链主导，而费米子Pfaffian则表现出与Pfaffian线丛和乐相关的全局反常，该反常由相对Rochlin不变量刻画。这些结果共同为非单连通靶群的WZW模型半经典定域化的拓扑贡献提供了统一描述。
英文摘要
We study the partition functions of Wess--Zumino--Witten (WZW) models with compact connected simple Lie group manifolds that are not simply connected. Starting from the modular-invariant partition function of Felder--Gawędzki--Kupiainen (FGK), we derive a localization formula, which can also be obtained directly by supersymmetric localization of the corresponding supersymmetric WZW model. Our results reveal a variety of topological effects associated with the nontrivial topology of the target group. In particular, the Wess--Zumino amplitude is governed by FGK cocycles, while the fermion Pfaffians exhibit global anomalies associated with the holonomies of Pfaffian line bundles, captured by relative Rochlin invariants. Together, these results provide a unified description of the topological contributions to the semiclassical localization of WZW models with non-simply connected target groups.
