Toric CFTs, permutation triples, and Belyi pairs
Toric CFTs, permutation triples, and Belyi pairs
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DOI：
10.1007/jhep03(2011)065
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发表时间：
2010-12
影响因子：
5.4
通讯作者：
Vishnu Jejjala;S. Ramgoolam;D. Rodríguez-Gómez
中科院分区：
文献类型：
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作者：
Vishnu Jejjala;S. Ramgoolam;D. Rodríguez-Gómez
四维CFTs对偶于横截于环面卡-丘三重的膜，已经用环面上的二分图（二聚体模型）来描述。我们使用dessins d 'enfants理论来用相乘为一的三重排列来描述这些。这些排列产生了一个优雅的描述之字形路径，这已经出现在表征的环形二聚体，导致一致的SCFT。Dessins也与Belyi对有关，由配备地图的曲线组成，在三个点上分支。我们构造了一些与CFTs相关的Belyi对的明确例子，包括和conifold。超势的置换对称性与Belyi对的几何有关。阿丁辫群作用及其变体起着有趣的作用。本文提出了一个关于Belyi曲线的复结构与共形场论中的R-荷的关系的猜想。
Four-dimensional CFTs dual to branes transverse to toric Calabi-Yau threefolds have been described by bipartite graphs on a torus (dimer models). We use the theory of dessins d’enfants to describe these in terms of triples of permutations which multiply to one. These permutations yield an elegant description of zig-zag paths, which have appeared in characterizing the toroidal dimers that lead to consistent SCFTs. The dessins are also related to Belyi pairs, consisting of a curve equipped with a map to, branched over three points on the. We construct explicit examples of Belyi pairs associated to some CFTs, includingand the conifold. Permutation symmetries of the superpotential are related to the geometry of the Belyi pair. The Artin braid group action and a variation thereof play an interesting role. We make a conjecture relating the complex structure of the Belyi curve to R-charges in the conformal field theory.