含缺陷的面积相关量子场论
Area-dependent quantum field theory with defects
摘要：
面积相关的量子场论是二维拓扑量子场论的一种修正，其中为边形的每个连通分量配备一个正的实数-解释为面积-在胶合下表现为加性。与拓扑理论相反，在面积相关理论中，状态空间可以是无限维的。我们介绍了正规化Frobenius代数的概念，并表明，面积相关的理论是在一对一的对应交换正规化Frobenius代数。我们提供了一个国家和建设面积依赖的理论，其中包括理论的缺陷。正则化代数上的亏线用可对偶双模标记。我们证明了这种双模的张量积与缺陷线的融合一致，缺陷线的融合定义为将两条缺陷线分开的面积取为零的极限。所有这些结构的例子是二维杨米尔斯理论与紧凑的规范群和威尔逊线作为缺陷，我们详细处理。
英文摘要：
Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number - interpreted as area - which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We provide a state-sum construction for area-dependent theories, which includes theories with defects. Defect lines are labeled by dualisable bimodules over regularised algebras. We show that the tensor product of such bimodules agrees with the fusion of defect lines, which is defined as the limit where the area separating two defect lines is taken to zero. All these constructions are exemplified by two-dimensional Yang-Mills theory with compact gauge group and with Wilson lines as defects, which we treat in detail.
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