Categories of quantum liquids III

Liang Kong; Hao Zheng

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arXiv · 2201.05726

Categories of quantum liquids III

Liang Kong·Hao Zheng

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Abstract

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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Liang Kong, Hao Zheng. 2022-01-15. Categories of quantum liquids III. https://arxiv.org/abs/2201.05726

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