标题： 2+1D拓扑序中的凝结完成与缺陷 显示英文标题

标题： Condensation Completion and Defects in 2+1D Topological Orders

摘要： 我们回顾模张量范畴的凝结完成，这会产生一个余维至少为1的缺陷的融合2-范畴，在$2+1$D拓扑序中。 我们将凝结完成应用于具有$2+1$D拓扑序和$\mathbb Z_2\times \mathbb Z_2$以及$\mathbb Z_4$融合规则的系统。 在这些情况下，我们明确列举出这些拓扑序中存在的$1$d和$0$d缺陷，以及它们的融合规则。 我们还讨论了凝聚完成的其他应用：对辫子融合范畴的凝聚完成的替代解释；对对称电荷范畴的凝聚完成及其与具有对称性的能隙相之间的对应关系；对于一个拓扑序$\mathcal{C}$，也可以通过计算$\mathcal{C}$的凝聚完成，找到$\mathcal{C}$与其时间反演共轭叠加的所有能隙边界。 显示英文摘要

摘要： We review the condensation completion of a modular tensor category, which yields a fusion 2-category of codimension-1 and higher defects in a $2+1$D topological order. We apply the condensation completion to $2+1$D topological order with $\mathbb Z_2\times \mathbb Z_2$ and $\mathbb Z_4$ fusion rules. In these cases, we explicitly enumerate the $1$d and $0$d defects present in these topological orders, along with their fusion rules. We also talk about other applications of condensation completion: alternative interpretations of condensation completion of a braided fusion category; condensation completion of the category of symmetry charges and its correspondence to gapped phases with symmetry; for a topological order $\mathcal{C}$, one can also find all gapped boundaries of the stacking of $\mathcal{C}$ with its time-reversal conjugate through computing the condensation completion of $\mathcal{C}$.