标题： 有限2-群规范理论及其3+1D晶格实现 显示英文标题

标题： Finite 2-group gauge theory and its 3+1D lattice realization

摘要： 在本工作中，我们使用Tannaka-Krein重构来计算有限2群$\mathcal G$的量子双代数$\mathcal D(\mathcal G)$，作为一个霍普夫单子范畴。 我们还从2群$\mathcal G$的Dijkgraaf-Witten拓扑量子场论函子构造了一个3+1D格点模型，推广了Kitaev的2+1D量子双代数模型。 值得注意的是，该格点模型中的类似弦的局部算符被证明形成$\mathcal D(\mathcal G)$。 专门针对$\mathcal G = \mathbb{Z}_2$，我们证明了3+1D拓扑码模型中的拓扑缺陷是$\mathcal D(\mathbb{Z}_2)$上的模。 显示英文摘要

摘要： In this work, we employ the Tannaka-Krein reconstruction to compute the quantum double $\mathcal D(\mathcal G)$ of a finite 2-group $\mathcal G$ as a Hopf monoidal category. We also construct a 3+1D lattice model from the Dijkgraaf-Witten TQFT functor for the 2-group $\mathcal G$, generalizing Kitaev's 2+1D quantum double model. Notably, the string-like local operators in this lattice model are shown to form $\mathcal D(\mathcal G)$. Specializing to $\mathcal G = \mathbb{Z}_2$, we demonstrate that the topological defects in the 3+1D toric code model are modules over $\mathcal D(\mathbb{Z}_2)$.