Modular Invariants, Graphs and α-Induction for Nets of Subfactors. II
Modular Invariants, Graphs and α-Induction for Nets of Subfactors. II
复制标题
子因子网络的模不变量、图和 α 归纳 II。
DOI：
10.1007/s002200050523
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发表时间：
1998
影响因子：
2.4
通讯作者：
David E. Evans
中科院分区：
文献类型：
--
作者：
Jens Böckenhauer;David E. Evans
摘要：我们将我们在上一篇论文中阐述的扇区α诱导理论应用于由保形场理论产生的几个子因子网。它的主要应用是SU(N)WZW模型的共形嵌入和奥布里奥德包含。对于后者，我们手工构造了扩展的因素网。进一步发展了F.Xu的一些想法，我们的处理规范地导致了某些融合图，并且在我们的所有例子中，我们重新发现了与相应的SU(N)模不变量经验地关联的图Di Francesco，Petkova和Zuber。我们建立了这些图的指数与块对角线模不变量中特征的出现之间的联系，前提是扩展的模S矩阵对角化了扩展理论的自同态融合规则。这在许多情况下都得到了证明，并且我们的结果涵盖了所有块对角线SU(2)模不变量，
从而对A-D-E的分类提供了一些解释。
Abstract:We apply the theory of α-induction of sectors which we elaborated in our previous paper to several nets of subfactors arising from conformal field theory. The main application are conformal embeddings and orbifold inclusions of SU(n) WZW models. For the latter, we construct the extended net of factors by hand. Developing further some ideas of F. Xu, our treatment leads canonically to certain fusion graphs, and in all our examples we rediscover the graphs Di Francesco, Petkova and Zuber associated empirically to the corresponding SU(n) modular invariants. We establish a connection between exponents of these graphs and the appearance of characters in the block-diagonal modular invariants, provided that the extended modular S-matrices diagonalize the endomorphism fusion rules of the extended theories. This is proven for many cases, and our results cover all the block-diagonal SU(2) modular invariants,
thus provide some explanation of the A-D-E classification.