The Kernel of the Modular Representation and the Galois Action in RCFT

The Kernel of the Modular Representation and the Galois Action in RCFT
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RCFT中模表示的内核和伽罗瓦动作

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发表时间：
2001
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通讯作者：
P. Bantay
P. Bantay
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文献类型：
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作者：
P. Bantay

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翻译后摘要：它表明，与有理共形场论的模块化表示，内核是一个同余子群，其水平等于德恩扭曲的顺序。 给出了该核的一个显式代数刻画。它还表明，德恩扭曲的顺序是有界的主要字段的数量的函数，允许来自RCFTs的模块化表示的系统枚举。限制的频谱的德恩扭曲和算术性质的模块矩阵元素。
Abstract: It is shown that for the modular representations associated to Rational Conformal Field Theories, the kernel is a congruence subgroup whose level equals the order of the Dehn-twist. An explicit algebraic characterization of the kernel is given. It is also shown that the order of the Dehn-twist is bounded by a function of the number of primary fields, allowing for a systematic enumeration of the modular representations coming from RCFTs. Restrictions on the spectrum of the Dehn-twist and arithmetic properties of modular matrix elements are presented.