Brane tilings and exceptional collections
Brane tilings and exceptional collections
复制标题
薄膜瓷砖和特殊系列
DOI：
10.1088/1126-6708/2006/07/001
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发表时间：
2006
影响因子：
5.4
通讯作者：
David Vegh
中科院分区：
文献类型：
--
作者：
A. Hanany;C. Herzog;David Vegh
膜平铺和例外集合都是描述低能规范理论的有用工具，它们是在一堆D3-膜上探测卡-丘奇异性的。我们提供了一本字典，可以在这两种迄今为止互不相关的语言之间进行翻译。给定一个膜平铺，我们计算一个特殊的收集线丛的基础上的非紧卡-丘三倍。给出一个例外的集合，我们得到了规范理论的周期性的周期性的，它是膜镶嵌的图论对偶。我们的结果给新的洞察力的建设的非线性理论及其关系的几何。
Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.