Non-Abelian localization for Chern-Simons theory
Non-Abelian localization for Chern-Simons theory
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Chern-Simons 理论的非阿贝尔定域化
DOI：
10.4310/jdg/1143642932
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发表时间：
2005
影响因子：
2.5
通讯作者：
E. Witten
中科院分区：
文献类型：
--
作者：
C. Beasley;E. Witten
我们重新考虑塞弗特流形 M（黎曼曲面上非平凡圆丛的总空间）上的陈-西蒙斯规范理论。当 M 是 Seifert 流形时，Lawrence 和 Rozansky 从 Chern-Simons 理论的精确解中证明，配分函数具有非常简单的结构，并且可以完全重写为 M 上平坦连接的局部贡献之和。我们解释了这一经验事实如何从应用于 Chern-Simons 路径积分的非阿贝尔局部化技术得出。在此过程中，我们证明 M 上的 Chern-Simons 理论的配分函数承认 M 上平面连接模空间的等变上同调的拓扑解释。
We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface). When M is a Seifert manifold, Lawrence and Rozansky have shown from the exact solution of Chern-Simons theory that the partition function has a remarkably simple structure and can be rewritten entirely as a sum of local contributions from the flat connections on M. We explain how this empirical fact follows from the technique of non-abelian localization as applied to the Chern-Simons path integral. In the process, we show that the partition function of Chern-Simons theory on M admits a topological interpretation in terms of the equivariant cohomology of the moduli space of flat connections on M.