AI 中文总结
研究对称丰富拓扑相中的任意子凝聚，通过扩展胡 - 吉尔 - 吴弦网模型，表明保持\(G\)的凝聚由多融合范畴的兼容分次表征，构建子SET相输入，并用三个量子双例子说明，还指出对称分数化任意子在特定条件下不阻碍凝聚。
AI 中文摘要
尽管任意子凝聚是关联拓扑序的标准机制，但对称丰富拓扑（SET）相中的任意子凝聚更为复杂，因为凝聚体还必须与全局对称性兼容。我们研究了由具有多融合范畴输入数据的扩展胡 - 吉尔 - 吴（HGW）弦网模型描述的SET相中的对称保持任意子凝聚。我们表明，保持\(G\)的凝聚由输入多融合范畴的兼容分次来表征，并且这种分次构建了子SET相的多融合范畴输入。为了使这种构建具体，我们考虑相关数据来自\(G\)由\(N\)的有限群扩张\(E\)的情况：一个\(E\)-分次融合范畴通过传递到商对称性\(G\)诱导出一个\(G\)-SET输入，并且所得输入自然带有兼容的\(N\)-分次，该分次在保持\(G\)的同时在SET相内实现进一步凝聚。我们用三个量子双例子说明了这种构建：平凡扩张\(\mathbb{Z}_2\times\mathbb{Z}_2\)、非阿贝尔半直积\(S_3\)和非平凡中心扩张\(\mathbb{Z}_4\)。\(\mathbb{Z}_4\)例子进一步表明，一旦将凝聚体视为物理相干态，对称分数化任意子不会阻碍对称保持凝聚。
英文摘要
Although anyon condensation is a standard mechanism for relating topological orders, anyon condensation in symmetry-enriched topological (SET) phases is more intricate because the condensate must also be compatible with the global symmetry. We study symmetry-preserving anyon condensation in SET phases described by the enlarged Hu-Geer-Wu (HGW) string-net model with multifusion-category input data. We show that a $G$-preserving condensation is characterized by a compatible grading of the input multifusion category, and that this grading constructs the multifusion-category input of the child SET phase. To make this construction concrete, we consider the case where the relevant data come from a finite group extension $E$ of $G$ by $N$: an $E$-graded fusion category induces a $G$-SET input by passing to the quotient symmetry $G$, and the resulting input naturally carries a compatible $N$-grading that implements the further condensation inside the SET phase while preserving $G$. We illustrate the construction using three quantum-double examples: the trivial extension $\mathbb{Z}_2\times\mathbb{Z}_2$, the non-Abelian semidirect product $S_3$, and the nontrivial central extension $\mathbb{Z}_4$. The $\mathbb{Z}_4$ example further shows that symmetry fractionalized anyons do not obstruct symmetry-preserving condensation once the condensate is treated as a physical coherent state.
Comments28 pages, 3 Figures
