发表机构
Xiamen University; Peng Huanwu Center for Fundamental Theory; Korea Advanced Institute of Science & Technology（厦门大学; 彭桓武理论研究中心; 韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为二维非可逆对称性建立一般框架，通过规范非阿贝尔对称性得到对偶理论，并给出配分函数正逆变换，测试于有限群并扩展至紧李群。
AI 中文摘要
我们研究了二维理论$\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$中的对偶量子对称性$\mathrm{Rep}(G)$，该理论是通过对$\mathfrak{T}_G$的非阿贝尔对称性$G$进行规范（对于李群$G$，规范理解为平坦规范）而获得的。我们发展了一个一般框架，用于在任意非可逆对称性背景下计算$\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}}$的配分函数，这些背景由$\mathrm{Rep}(G)$的拓扑缺陷网络表示，并且用原始理论$\mathfrak{T}_G$的配分函数来表达。我们还推导了逆变换，将$\mathfrak{T}_G$在$G$背景下的配分函数用$\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$的配分函数表示。我们在几个例子中测试了该框架，包括具有无多重性和高多重性融合规则的有限群，并讨论了向紧李群的形式扩展，重点关注$\mathrm{Rep}(SU(2))$。
英文摘要
We study the dual quantum symmetry $\mathrm{Rep}(G)$ in the two-dimensional theory $\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$ obtained by gauging a non-abelian symmetry $G$ of $\mathfrak{T}_G$, where for Lie groups $G$ the gauging is understood as flat gauging. We develop a general framework for computing partition functions of $\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$ in arbitrary non-invertible symmetry backgrounds, represented by topological defect networks of $\mathrm{Rep}(G)$, in terms of the partition functions of the original theory $\mathfrak{T}_G$. We also derive the inverse transformation, expressing partition functions of $\mathfrak{T}_G$ in $G$ backgrounds in terms of those of $\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$. We test the framework in several examples, including finite groups with multiplicity-free and higher-multiplicity fusion rules, and discuss a formal extension to compact Lie groups, focusing on $\mathrm{Rep}(SU(2))$.
