Decomposition, trivially-acting symmetries, and topological operators
Decomposition, trivially-acting symmetries, and topological operators
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DOI：
10.1103/physrevd.107.085017
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发表时间：
2022-11
影响因子：
5
通讯作者：
D. Robbins;E. Sharpe;T. Vandermeulen
中科院分区：
文献类型：
--
作者：
D. Robbins;E. Sharpe;T. Vandermeulen
二维共形场论中的平凡作用对称性包括零维扭转场，它们是局部拓扑算子。我们研究了将这些算子作为理论全局对称性的一部分的结果。也就是说，我们将这种对称性视为拓扑缺陷线（tdl）和拓扑点算子（TPOs）的混合。由平凡作用对称相关的tdl可以在TPO处连接，形成非平凡的双向结。经过测量，这些结点处的局部算符可以在一个不相交的理论联合中变成真空。因此，在测量下检查tpo的行为使我们能够通过跟踪每个宇宙的琐碎作用对称性来改进分解。tdl和tpo之间的混合异常为这些轨道的配分函数提供了离散的类扭转相，修改了最终的分解。这个框架也很容易考虑到平凡作用的不可逆对称性。
Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry of the theory. That is, we regard such a symmetry as a mix of topological defect lines (TDLs) and topological point operators (TPOs). TDLs related by a trivially-acting symmetry can join at a TPO to form non-trivial two-way junctions. Upon gauging, the local operators at those junctions can become vacua in a disjoint union of theories. Examining the behavior of the TPOs under gauging therefore allows us to refine decomposition by tracking the trivially-acting symmetries of each universe. Mixed anomalies between the TDLs and TPOs provide discrete torsion-like phases for the partition functions of these orbifolds, modifying the resulting decomposition. This framework also readily allows for the consideration of trivially-acting non-invertible symmetries.