arXiv 0911.26872009-11hep-thmath.GTmath.SG

Chern-Simons理论中威尔逊圈的局部化

Localization for Wilson Loops in Chern-Simons Theory

Chris Beasley

备注：: 227 pages, 1 figure, harvmac, v2: references added
发表信息：: Adv. Theor. Math. Phys. 17 (2013) 1-240

摘要：

我们重新考虑塞弗特流形M上的陈-西蒙斯规范理论，塞弗特流形M是黎曼曲面上的非平凡圆丛的全空间，可能有轨道点。如Witten在以前的工作中所示，非阿贝尔局部化的路径积分技术可以用来表示Chern-Simons理论的配分函数，它表示为M上平坦联络的模空间的等变上同调。这里我们把这个结果推广到缠绕M的圆纤维的威尔逊圈算子的期望值。在局部化条件下，这样的威尔逊圈算子自然地退化为模空间上的一个相关泛丛的陈特征标。一路上，我们证明了威尔逊圈路径积分的定相近似是精确的环面结，经验的观察劳伦斯和Rozansky之前，这项工作。

英文摘要：

We reconsider Chern-Simons gauge theory on a Seifert manifold M, which is the total space of a nontrivial circle bundle over a Riemann surface, possibly with orbifold points. As shown in previous work with Witten, the path integral technique of non-abelian localization can be used to express the partition function of Chern-Simons theory in terms of the equivariant cohomology of the moduli space of flat connections on M. Here we extend this result to apply to the expectation values of Wilson loop operators which wrap the circle fibers of M. Under localization, such a Wilson loop operator reduces naturally to the Chern character of an associated universal bundle over the moduli space. Along the way, we demonstrate that the stationary-phase approximation to the Wilson loop path integral is exact for torus knots, an observation made empirically by Lawrence and Rozansky prior to this work.

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