Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories
Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories
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DOI：
10.1088/1751-8121/ab8e03
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发表时间：
2019-12
期刊：
影响因子：
--
通讯作者：
J. Harvey;Yichen Hu;Yuxiao Wu
中科院分区：
文献类型：
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作者：
J. Harvey;Yichen Hu;Yuxiao Wu
Hecke算子将具有不同中心荷的有理共形场论（RCFTs）的特征联系起来，并扩展了模表示和融合代数的伽罗瓦对称性.我们表明，导体N的RCFT和模N的二次剩余发挥重要作用的计算和分类的伽罗瓦置换。通过有效中心电荷的图像，结合伽罗瓦内自同构和简单电流的结构，我们建立了不同理论中的场对应。然后，我们首次尝试将Hecke算子扩展到模张量范畴的全部数据。模块化数据中遇到的伽罗瓦对称性也变换了融合矩阵和编织矩阵，并在Hecke算子相关的理论中产生同构结构。
Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor N of an RCFT and the quadratic residues modulo N play an important role in the computation and classification of Galois permutations. We establish a field correspondence in different theories through the picture of effective central charge, which combines Galois inner automorphisms and the structure of simple currents. We then make a first attempt to extend Hecke operators to the full data of modular tensor categories. The Galois symmetry encountered in the modular data transforms the fusion and the braiding matrices as well, and yields isomorphic structures in theories related by Hecke operators.