Rational CFT with three characters: the quasi-character approach
Rational CFT with three characters: the quasi-character approach
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DOI：
10.1007/jhep05(2020)003
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发表时间：
2020-05-04
影响因子：
5.4
通讯作者：
Singh, Palash
中科院分区：
文献类型：
--
作者：
Mukhi, Sunil;Poddar, Rahul;Singh, Palash
准字符是向量值模函数，具有积分，但不一定是正的q展开。使用模微分方程，在arXiv:1810.09472中提供了两个字符的完整分类。这些依次生成所有可能的字符，任意朗斯基索引，顺序为2。在这里，我们开始对三字案例进行研究。我们推测了几个无限族的拟字符，并通过实例证明了它们的线性组合可以产生具有任意大朗斯基指数的可容许字符。该结构与二阶情况完全不同，arXiv:1602.01022的新颖协集结构对发现合适的家族起着关键作用。利用偶非模格，构造了与新容许字符对应的显式三字符CFT。
Quasi-characters are vector-valued modular functions having an integral, but not necessarily positive, q-expansion. Using modular differential equations, a complete classification has been provided in arXiv:1810.09472 for the case of two characters. These in turn generate all possible admissible characters, of arbitrary Wronskian index, in order two. Here we initiate a study of the three-character case. We conjecture several infinite families of quasi-characters and show in examples that their linear combinations can generate admissible characters with arbitrarily large Wronskian index. The structure is completely different from the order two case, and the novel coset construction of arXiv:1602.01022 plays a key role in discovering the appropriate families. Using even unimodular lattices, we construct some explicit three-character CFT corresponding to the new admissible characters.