标题： 类别异常匹配 显示英文标题

标题： Categorical Anomaly Matching

摘要： 匹配't Hooft反常是约束量子系统低能动力学及其允许的重整化群(RG)流的强大工具。 然而，对于非可逆（或范畴）对称性，一个关键挑战是缺乏精确的框架来表征和量化反常。 我们通过将紫外(UV)和红外(IR)对称性范畴之间的张量函子确定为捕捉这些约束的核心来解决这个问题。 为此，我们引入了异常简单范畴(ASCies)作为范畴反常的基本构建块。 给定的对称性范畴可能支持多个ASCies，每个都编码不同的异常特征。 这些结构在对称拓扑场理论(SymTFT)的背景下自然出现，其中张量函子对应于UV和IR SymTFT之间的RG界面，而ASCies作为满足简单普遍条件的特定此类界面实现。 我们通过涉及不同时空维度中的异常0-形式、高阶形式以及关键的非可逆对称性的例子来展示该框架的实用性。 显示英文摘要

摘要： Matching 't Hooft anomalies is a powerful tool for constraining the low-energy dynamics of quantum systems and their allowed renormalization group (RG) flows. For non-invertible (or categorical) symmetries, however, a key challenge has been the lack of a precise framework to characterize and quantify anomalies. We address this by identifying tensor functors between UV and IR symmetry categories as central to capturing these constraints. To this end, we introduce Anomalous Simple Categories (ASCies) as fundamental building blocks of categorical anomalies. A given symmetry category may support multiple ASCies, each encoding distinct anomalous features. These structures naturally arise in the context of the Symmetry Topological Field Theory (SymTFT), where tensor functors correspond to RG-interfaces between UV and IR SymTFTs, and ASCies are realized as particular such interfaces satisfying simple, universal criteria. We demonstrate the utility of this framework through examples involving anomalous 0-form, higher-form, and crucially, non-invertible symmetries in various spacetime dimensions.