Graded quivers, generalized dimer models and toric geometry
Graded quivers, generalized dimer models and toric geometry
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DOI：
10.1007/jhep11(2019)104
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发表时间：
2019-04
影响因子：
5.4
通讯作者：
S. Franco;A. Hasan
中科院分区：
文献类型：
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作者：
S. Franco;A. Hasan
CY（m+ 2）-折叠上拓扑B-模型的开弦扇区由具有超势的m-分次箭图描述.这种对应关系将CY（m+ 2）-折叠与D（5− 2 m）-膜的世界体积（m= 0，...，3）上的规范理论之间的著名联系推广到一般的m。在CY（m+ 2）-折叠是复曲面的情况下，我们引入了m-二聚体，它完全编码了m-分次箭图及其超势.推广众所周知的m= 1、2的情况，m-二聚体显着简化了几何与m-分次颤动之间的联系。本文的一个关键结果是推广的完美匹配的概念，这在这个地图中起着核心作用，任意m。我们还介绍了一个简化的算法计算完美匹配，推广Kasteleyn矩阵的方法，任何m。我们说明这些新的工具与几个无限的家庭CY奇点。
The open string sector of the topological B-model on CY (m+ 2)-folds is de-scribed by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m+ 2)-folds and gauge theories on the world-volume of D (5− 2m)-branes for m= 0,…, 3. We introduce m-dimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+ 2)-folds are toric. Generalizing the well known m= 1, 2 cases, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key result of this paper is the generalization of the concept of perfect matching, which plays a central role in this map, to arbitrary m. We also introduce a simplified algorithm for the computation of perfect matchings, which generalizes the Kasteleyn matrix approach to any m. We illustrate these new tools with a few infinite families of CY singularities.