量子液体的分类III
Categories of quantum liquids III
摘要：
我们继续我们的研究类别的量子液体开始在以前的工作。我们结合局部量子对称性与拓扑骨架到一个单一的数学理论的拓扑网和缺陷网。特别是，我们介绍了拓扑网络的概念，这是从共形网的动机和推广，和缺陷网的概念，推广共形网之间的缺陷。我们给出了明确的例子。此外，我们构造了由余维$k$的亏$n$ -网定义的具有$k$ -态射的拓扑$n$ -网范畴，并证明了$n$ D量子液体范畴可以从中提取出来，并通过拓扑网的凝聚理论显式计算.
英文摘要：
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.
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