Graded quivers and B-branes at Calabi-Yau singularities
Graded quivers and B-branes at Calabi-Yau singularities
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卡拉比-丘奇点处的分级箭袋和 B 膜
DOI：
10.1007/jhep03(2019)053
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发表时间：
2019
影响因子：
5.4
通讯作者：
Hasan, Azeem
中科院分区：
文献类型：
--
作者：
Closset, Cyril;Franco, Sebastián;Guo, Jirui;Hasan, Azeem
一个具有超势的分次幂函数是一个幂函数，它的箭头被赋以度c ∈ {0，1，n，m}，对于某个整数m ≥ 0，其关系由一个m − 1次的超势生成。普通箭图（m = 1）通常描述D-膜系统的开弦扇区;特别是，它们以4d = 1超对称的超规范理论的幌子，在IIB型弦理论中捕捉了D3-膜在局部卡-丘（CY）3重奇点处的物理学。最近有人指出，m = 2和m = 3的分次箭图类似地描述了CY 4重和5重奇点的D膜系统，分别为2d =（0，2）和0d = 1规范理论。在这项工作中，我们进一步探讨了m-分次箭图与超势Q（m）和CY（m +2）-折叠奇点X m +2之间的对应关系。对于任意的m，X m +2上拓扑B模型的开弦扇区可以用分次π来描述。我们说明了这种对应关系明确与一些无限家庭的复曲面奇点索引m ∈ π，我们得出"复曲面"分级箭图的几何形状，使用几个互补的观点。超对称规范理论的许多有趣的方面可以形式上扩展到任何m;例如，对于一族奇点，称为C（Y 1，0（m）），它将锥状奇点推广到m> 1，我们指出对应的分次箭图存在形式上的"对偶级联"。
A graded quiver with superpotential is a quiver whose arrows are assigned degrees c∈{0, 1,⋯, m}, for some integer m≥ 0, with relations generated by a superpotential of degree m− 1. Ordinary quivers (m= 1) often describe the open string sector of D-brane systems; in particular, they capture the physics of D3-branes at local Calabi-Yau (CY) 3-fold singularities in type IIB string theory, in the guise of 4d= 1 supersymmetric quiver gauge theories. It was pointed out recently that graded quivers with m= 2 and m= 3 similarly describe systems of D-branes at CY 4-fold and 5-fold singularities, as 2d=(0, 2) and 0d= 1 gauge theories, respectively. In this work, we further explore the correspondence between m-graded quivers with superpotential, Q (m), and CY (m+ 2)-fold singularities, X m+ 2. For any m, the open string sector of the topological B-model on X m+ 2 can be described in terms of a graded quiver. We illustrate this correspondence explicitly with a few infinite families of toric singularities indexed by m∈ ℕ, for which we derive “toric” graded quivers associated to the geometry, using several complementary perspectives. Many interesting aspects of supersymmetric quiver gauge theories can be formally extended to any m; for instance, for one family of singularities, dubbed C (Y 1, 0 (ℙ m)), that generalizes the conifold singularity to m> 1, we point out the existence of a formal “duality cascade” for the corresponding graded quivers.
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