论文标题
不可变形的对称性和更高的表示理论II
Non-invertible Symmetries and Higher Representation Theory II
论文作者
论文摘要
在本文中，我们继续调查对全球分类对称性的调查，这些对称性在测量有限的高层群体及其较高的亚组中以离散的扭转。动机是提供关于在更高维度中构建不可矛盾的全球对称性以及对相关对称类别的精确描述的共同观点。我们建议，通过测量较高的亚组获得的对称类别可以定义为较高的群体理论融合类别，这些类别是由较高组的较高表示形式构建的。作为具体应用，我们提供了基于Lie代数$ \ Mathfrak {so}（n）$的三个维度和四个维度的对称性类别的统一描述，以及通过与混合't Hooft'T Hooft't Hooft Anomaly获得的1型对称性获得的对1型对称性获得的不可违反对称性的完全分类描述。我们还讨论了离散扭转对对称类别的影响，这是一系列由光谱序列参数确定的障碍物。
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete applications we provide a unified description of the symmetry categories of gauge theories in three and four dimensions based on the Lie algebra $\mathfrak{so}(N)$, and a fully categorical description of non-invertible symmetries obtained by gauging a 1-form symmetry with a mixed 't Hooft anomaly. We also discuss the effect of discrete torsion on symmetry categories, based a series of obstructions determined by spectral sequence arguments.
