arXiv 1402.31402014-02-13hep-thmath-phmath.MP

阿贝尔Chern-Simons理论中的路径积分不变量

Path-integral invariants in abelian Chern-Simons theory

Enore Guadagnini, Frank Thuillier

发表信息：: Nucl.Phys. B882 (2014) 450-484
DOI：: 10.1016/j.nuclphysb.2014.03.009

摘要：

考虑了一般闭定向三维流形$M$中的$U(1)$ Chern-Simons规范理论，利用泛函积分计算了规范化配分函数和链完整性的期望值.非微扰路径积分定义在属于$M$上各种不等价的$U(1)$主丛的连接的规范轨道空间中;位形空间的不同扇区由$M$的第一同调群的元素标记，并由适当的背景连接表征。平坦连接的规范轨道，其分类也是基于同调群，控制非微扰贡献的平均值的程度。在任意3维$M$中实现了函数积分，相应的路径积分不变量与交换的Reshetikhin-Turaev外科手术不变量严格相关.

英文摘要：

We consider the $U(1)$ Chern-Simons gauge theory defined in a general closed oriented 3-manifold $M$; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The nonperturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent $U(1)$ principal bundles over $M$; the different sectors of the configuration space are labelled by the elements of the first homology group of $M$ and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the extent of the nonperturbative contributions to the mean values. The functional integration is achieved in any 3-manifold $M$, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin-Turaev surgery invariants.

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