二维辫子量子自旋系统的超选择理论：基于Connes融合
Superselection theory for 2D braided quantum spin systems via Connes fusion
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中文总结 AI 辅助
本文利用Connes融合张量积，在不局域化的情况下构造了二维辫子量子自旋系统超选择扇区的等价辫子张量结构，并证明其与酉辫子融合范畴的ind-完备化反范畴等价。
中文摘要 AI 辅助
文章arXiv:2410.21454利用局域化且可输运的自同态，在适当几何偏序集上的冯·诺依曼代数网络上构造了超选择扇区的辫子$\text{W}^*$-张量范畴。本文借鉴arXiv:1812.04470中关于共形网的思想，在不进行局域化的前提下，利用Connes融合张量积构造了等价的张量积与辫子结构。作为应用，我们证明了由arXiv:2506.19969中酉辫子融合范畴$\text{Hilb}(\text{B})^{\text{op}}$构造的二维辫子量子自旋系统所关联的超选择扇区范畴，作为辫子$\text{W}^*$-张量范畴，等价于$\text{Hilb}(\text{B})^{\text{op}}$，即$\text{B}$的酉ind-完备化的反范畴。
英文摘要
The article arXiv:2410.21454 constructed a braided $\mathrm{W^*}$-tensor category of superselection sectors associated to a net of von Neumann algebras on a suitably geometric poset using localized and transportable endomorphisms. In this article, we construct an equivalent tensor product and braiding using the Connes fusion tensor product without localizing, using ideas from arXiv:1812.04470 for conformal nets. As an application, we prove that the category of superselection sectors associated to the 2D braided quantum spin system constructed from a unitary braided fusion category $\mathcal{B}$ in arXiv:2506.19969 is equivalent to $\mathsf{Hilb}(\mathcal{B})^{\rm op}$, the opposite of the unitary ind-completion of $\mathcal{B}$, as a braided $\mathrm{W^*}$-tensor category.
