论文标题
不可变形的对称性和更高的代表理论i
Non-invertible Symmetries and Higher Representation Theory I
论文作者
论文摘要
本文的目的是调查在三个或多个维度中测量有限较高组时出现的全球分类对称性。动机是在更高维度中对不可矛盾的全局对称性的构建以及相关对称类别的精确描述提供共同的观点。本文的重点是在三个维度上衡量有限群和2组。除了拓扑威尔逊线外，我们还表明，这会产生丰富的拓扑表面缺陷，并由2个陈述标记，并解释了它们与威尔逊线的冷凝缺陷的联系。我们得出了拓扑缺陷的各种特性，并表明关联的对称类别是2个分量的融合2类。这使我们能够通过断开仪表组确定某些仪表理论的完整对称类别。随后的论文将检查更高维度的更高较高群体的衡量。
The purpose of this paper is to investigate the global categorical symmetries that arise when gauging finite higher groups in three or more dimensions. The motivation is to provide a common perspective on constructions of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. This paper focusses on gauging finite groups and split 2-groups in three dimensions. In addition to topological Wilson lines, we show that this generates a rich spectrum of topological surface defects labelled by 2-representations and explain their connection to condensation defects for Wilson lines. We derive various properties of the topological defects and show that the associated symmetry category is the fusion 2-category of 2-representations. This allows us to determine the full symmetry categories of certain gauge theories with disconnected gauge groups. A subsequent paper will examine gauging more general higher groups in higher dimensions.
