Classification of local conformal nets. Case c < 1
Classification of local conformal nets. Case c < 1
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DOI：
10.4007/annals.2004.160.493
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发表时间：
2002-01
影响因子：
4.9
通讯作者：
Yasuyuki Kawahigashi;R. Longo
中科院分区：
文献类型：
--
作者：
Yasuyuki Kawahigashi;R. Longo
本文对中心荷c小于1的圆上vonNeumann代数的同构协变局部网进行了完全分类。不可约图与A-D 2n-E 6，8 Dynkin图对是双射对应的，使得它们的Coxeter数之差等于1。我们首先确定由c < 1的Virasoro代数的不可约表示与某些陪集网生成的网。然后，利用Cappelli-Itzykson-Zuber对极小模型的模不变量的分类和子因子理论中的α-归纳法，对c < 1的Virasoro网的所有局部不可约扩张进行了分类，并推导出了我们的主要分类结果.作为一个应用程序，我们确定在我们的分类列表中的某些具体陪集网在文献中研究。
We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs of A-D 2n -E 6,8 Dynkin diagrams such that the difference of their Coxeter numbers is equal to 1. We first identify the nets generated by irreducible representations of the Virasoro algebra for c < 1 with certain coset nets. Then, by using the classification of modular invariants for the minimal models by Cappelli-Itzykson-Zuber and the method of α-induction in subfactor theory, we classify all local irreducible extensions of the Virasoro nets for c < 1 and infer our main classification result. As an application, we identify in our classification list certain concrete coset nets studied in the literature.