The beta ansatz: a tale of two complex structures
The beta ansatz: a tale of two complex structures
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DOI：
10.1007/jhep06(2011)056
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发表时间：
2011-04
影响因子：
5.4
通讯作者：
A. Hanany;Yang-Hui He;Vishnu Jejjala;J. Pašukonis;S. Ramgoolam;D. Rodríguez-Gómez
中科院分区：
文献类型：
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作者：
A. Hanany;Yang-Hui He;Vishnu Jejjala;J. Pašukonis;S. Ramgoolam;D. Rodríguez-Gómez
膜镶嵌（英语：Brane tilings），有时也称为二聚体模型，是一类在环面上的二分图，它编码了四维SCFT的规范理论数据，这些SCFT与D3-膜对偶，探测环面的卡-丘三重。一个有效的编码方式，这些信息利用理论的dessin d 'enfants，表示的结构方面的置换三元组，这是反过来有关的一个Belyi对，即全纯映射从环面到awith三个标记点。在二聚体的等径嵌入的背景下，a-最大化的过程也将复杂结构与环面相关联，由SCFT中的R-电荷确定，这可以与Belyi复杂结构相比较。算法的显式建设的Belyi对进行了详细说明。在orbifolds的情况下，这些算法涉及到建设覆盖的椭圆曲线，它利用性质的Weierstravel椭圆函数。我们提出了一个反例，以前的猜想确定复杂的结构的Belyi曲线的复杂结构与R-收费。
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi-Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d’enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to awith three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstraß elliptic functions. We present a counter example to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges.