AI 中文总结
该研究分析了受2-群1-形式子群荷电的线的普适约束，发现其通常破缺0-形式对称性，由族反常强制执行，利用Wess-Zumino条件等工具研究了不同类型2-群的族反常及相关算符。
AI 中文摘要
2-群整体对称性以有趣的方式交织了0-形式和1-形式对称性。我们分析了受2-群的1-形式子群荷电的线的普适约束，证明这些线通常会明显破坏0-形式对称性。这产生了由破缺对称性生成元参数化的一族线缺陷，其存在性在体-缺陷系统的重整化群流下保持不变。这种对称性破缺由“族反常”强制执行，它是对称缺陷的拓扑障碍。我们的主要工具是Wess-Zumino一致性条件，以及适用于缺陷和边界的广义反常流入形式论。对于非阿贝尔连续2-群，族反常源于缺陷模空间上的高阶Berry联络，并约束探测破缺对称性局域作用的响应函数。在连续阿贝尔情形下，我们将微分上同调应用于2-群背景场，揭示了Wess-Zumino条件的微妙推广；而在离散情形下，我们将其重新表述为对称性缺陷的结合性问题。我们给出了大量说明性例子，尽可能计算了倾斜算（探测缺陷对破缺对称性的线性响应）及其高阶类似物的显式形式，这些对匹配族反常至关重要。我们还讨论了普适特征，如荷电线缺陷的对称性破坏如何与体中的对称性破缺层级相关，并强调了若干微妙要点，包括简单线与非简单线的区别以及Postnikov类的分解。
英文摘要
2-group global symmetries intertwine 0-form and 1-form symmetries in an interesting way. We analyze universal constraints on lines which are charged under the 1-form subgroup of a 2-group, and show that they generically break the 0-form symmetry explicitly. This gives rise to a family of line defects parameterized by the broken symmetry generators, whose existence is invariant under the renormalization group flow of the bulk-defect system. The symmetry breaking is enforced by a `family anomaly,' which is a topological obstruction to a symmetric defect. Our main tools are the Wess-Zumino consistency condition and a generalized anomaly inflow formalism for defects and boundaries. For nonabelian continuous 2-groups the family anomaly stems from a higher Berry connection on the moduli space of defects, and constrains response functions that probe the local action of the broken symmetry. In the continuous abelian case we apply differential cohomology to the 2-group background fields to uncover a subtle generalization of the Wess-Zumino condition, while in the discrete case we recast it in terms of the associativity of symmetry defects. We give numerous illustrative examples, computing when possible explicit forms of the tilt operator (which probes the linear response of the defect to the broken symmetry) and its higher analogs, which are crucial for matching the family anomaly. We also discuss universal features such as how symmetry violation by charged line defects is related to symmetry breaking hierarchies in the bulk, and highlight a number of subtle points including the distinction between simple and non-simple lines, and Postnikov class resolution.
Comments100 pages
