论文标题
不可变形的高级对称性
Non-Invertible Higher-Categorical Symmetries
论文作者
论文摘要
我们在较高类别的数据中绘制一个程序，以捕获D维量子场理论的一般不可矛盾的对称性，该图捕获了与对称性相关的拓扑缺陷的局部特性。我们还讨论了拓扑缺陷的融合，其中涉及在拓扑缺陷的世界化中局部的较高分类对称性的凝结/测量值。最近，在文献中讨论了一些拓扑缺陷的融合，拓扑缺陷的维度似乎在融合下跃升。这在高等法类别的标准描述中不可能。我们解释说，改变维度的融合被理解为描述对称性的高级较高的融合。我们还讨论了如何测量高级对称性的0形式亚对称性，并描述测量后获得的理论的较高分类对称性。这提供了一个程序，用于构建从可逆的高架或高层对称性开始并测量0形式的对称性开始的不可逆转性较高分类对称性。我们通过在4D仪表理论中构建不可固化的2类分类对称性以及5D和6D理论中的不可固化的3类别对称性来说明此过程。我们使用我们的方法检查了一些基于“ T HOOFT异常的方法”获得的结果，以检查一些结果。
We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also discuss fusions of topological defects, which involve condensations/gaugings of higher-categorical symmetries localized on the worldvolumes of topological defects. Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion. This is not possible in the standard description of higher-categories. We explain that the dimension-changing fusions are understood as higher-morphisms of the higher-category describing the symmetry. We also discuss how a 0-form sub-symmetry of a higher-categorical symmetry can be gauged and describe the higher-categorical symmetry of the theory obtained after gauging. This provides a procedure for constructing non-invertible higher-categorical symmetries starting from invertible higher-form or higher-group symmetries and gauging a 0-form symmetry. We illustrate this procedure by constructing non-invertible 2-categorical symmetries in 4d gauge theories and non-invertible 3-categorical symmetries in 5d and 6d theories. We check some of the results obtained using our approach against the results obtained using a recently proposed approach based on 't Hooft anomalies.
