Modular invariants and subfactors
Modular invariants and subfactors
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模不变量和子因子
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
David E. Evans
中科院分区：
文献类型：
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作者：
Jens Boeckenhauer;David E. Evans
在这个讲座中，我们解释了共形场论中的模不变量和算子代数中的辫子子因子之间的密切关系。我们的分析是基于一种方法，模块化的不变量使用编织部门的感应（“$阿尔法$感应”）所产生的治疗共形场理论中的Doplicher-Haag-Roberts框架。模不变量的许多性质，迄今已注意到经验和神秘的，可以严格推导出一个非常一般的设置在子因子的上下文中。例如，模不变量和图之间的联系（参见。SU（2）k）A-D-E分类找到了一个自然的解释和说明。我们试图给出一个概述目前的事态有关的预期等价的分类之间的辫子子因子和模块不变的二维共形场论。
In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction ("$alpha$-induction") arising from the treatment of conformal field theory in the Doplicher-Haag-Roberts framework. Many properties of modular invariants which have so far been noticed empirically and considered mysterious can be rigorously derived in a very general setting in the subfactor context. For example, the connection between modular invariants and graphs (cf. the A-D-E classification for $SU(2)_k$) finds a natural explanation and interpretation. We try to give an overview on the current state of affairs concerning the expected equivalence between the classifications of braided subfactors and modular invariant two-dimensional conformal field theories.