AI 中文总结
研究具有立方‘t Hooft反常理论中规范对称性时出现的对称结构，通过规范A×B产生含对偶对称性凝聚缺陷的对称结构，其缺陷产生可逆对称性扩展C，还描述了相关算符、态并举例说明。
AI 中文摘要
我们讨论了一类在一般时空维度中的对称结构，它出现在具有立方‘t Hooft反常的理论中规范对称性时。该反常将两个阿贝尔离散对称性A和B与另一个对称性C的特征类混合，我们规范A×B。此构造的新颖之处在于，所得对称结构涉及对偶对称性\(\widehat{A}\times\widehat{B}\)的某些凝聚缺陷。具体而言，这些缺陷产生一个可逆对称性，它根据特征类作为普通群扩展或高阶群扩展来扩展C。我们描述了相应的带电算符和态，并在几个例子中说明了该机制。
英文摘要
We discuss a class of symmetry structures in general spacetime dimension that arise when gauging symmetries in theories with a cubic 't Hooft anomaly. The anomaly mixes two Abelian discrete symmetries $A$ and $B$ with a characteristic class for an additional symmetry $C$, and we gauge $A\times B$. The novelty of this construction is that the resulting symmetry structure involves certain condensation defects of the dual symmetry $\widehat{A}\times\widehat{B}$. Specifically, these defects generate an invertible symmetry that extends $C$, either as an ordinary group extension or as a higher-group, depending on the characteristic class. We describe the corresponding charged operators and states, and illustrate the mechanism in several examples.
Comments37 pages + appendices, 22 figures, 1 table. v2: typos corrected, references and acknowledgments added
