论文标题
量子液体类别III
Categories of quantum liquids III
论文作者
论文摘要
我们继续研究量子液体类别的先前工作。我们将局部量子对称性与拓扑骨架结合在一起，成为拓扑网和缺陷网的单个数学理论。特别是，我们介绍了拓扑网的概念，拓扑网是由保形网的动机和概括的，以及缺陷网的概念，该概念概括了保形网络之间缺陷的概念。我们给出明确的例子。此外，我们构建了由$ k $ n $ n $ nets的类别，这些类别由$ k $ - 杂种，由缺陷$ n $ n $ nets condimension $ k $定义，并表明可以从中提取$ n $ d量子液体的类别，并通过拓扑网的浓缩理论从中提取并明确地计算出来。
We continue our study of the categories of quantum liquids started in a previous work. We combine local quantum symmetries with topological skeletons into a single mathematical theory of topological nets and defect nets. In particular, we introduce the notion of a topological net, which is motivated from and generalizes that of a conformal net, and the notion of a defect net which generalizes that of a defect between conformal nets. We give explicit examples of them. Moreover, we construct the category of topological $n$-nets with $k$-morphisms defined by defect $n$-nets of codimension $k$, and show that the category of $n$D quantum liquids can be extracted from it and computed explicitly via the condensation theory of topological nets.
