arXiv 1907.047342019-07hep-thmath-phmath.DGmath.MPmath.QA

二维Yang-Mills理论的对称性缺陷和轨道折叠

Symmetry defects and orbifolds of two-dimensional Yang-Mills theory

Lukas Müller, Richard J. Szabo, Lóránt Szegedy

备注：: 51 pages, 1 table, lots of figures; v2: references added; Final version to be published in Letters in Mathematical Physics

摘要：

我们描述了具有规范群$G$的二维Yang-Mills理论的离散对称性及其相应的缺陷，规范群与$G$的外自同构相关联。我们证明了含缺陷的规范理论配分函数可以用扭曲$G$ -丛空间上的路径积分来计算，并且得到了精确的计算结果。我们证明了它的弱耦合极限计算了曲面上平坦扭曲$G$ -丛的模空间的辛体积。利用亏损网络方法的广义orbifolds，我们规范的离散对称性和构造相应的orbifolds理论，这也是二维杨米尔斯理论，但与规范群给出的$G$的外自同构的扩展。借助于二维Yang-Mills理论拓扑亏损双范畴的轨道完备化，我们描述了离散规范对称性的Wilson线亏损的逆轨道.我们提出我们的结果使用两种互补的方法：在晶格正则化的路径积分，并在函子的方法，面积相关的量子场论的缺陷，通过正则化Frobenius代数。

英文摘要：

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted $G$-bundles, and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted $G$-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, which is again two-dimensional Yang-Mills theory but with gauge group given by an extension of $G$ by outer automorphisms. With the help of the orbifold completion of the topological defect bicategory of two-dimensional Yang-Mills theory, we describe the reverse orbifold using a Wilson line defect for the discrete gauge symmetry. We present our results using two complementary approaches: in the lattice regularisation of the path integral, and in the functorial approach to area-dependent quantum field theories with defects via regularised Frobenius algebras.

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英文摘要：

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