Matrix Model Superpotentials and Calabi-Yau Spaces: an ADE Classification
Matrix Model Superpotentials and Calabi-Yau Spaces: an ADE Classification
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矩阵模型超势和 Calabi-Yau 空间：ADE 分类
DOI：
--
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
C. Curto
中科院分区：
文献类型：
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作者：
C. Curto
我们使用F。Ferrari的方法将矩阵模型与Calabi-Yau空间联系起来，以解释$\N=1$超共形理论的Intriligator和Wecht的ADE分类，这些理论作为$\N = 1$ SQCD理论的RG不动点与伴随点出现。矩阵模型和$\N = 1$规范理论之间的联系可以被看作是Dijkgraaf-Vafa猜想的证据。我们发现，ADE超势在Intriligator-Wecht分类完全匹配矩阵模型超势从Calabi-Yau的相应ADE奇点。此外，在附加的$\Hat{O}，\Hat{A}，\Hat{D}$和$\Hat{E}$情形中，我们发现了新的奇异几何.这些“帽子”的几何形状是密切相关的ADE对应，但功能非孤立的奇点。作为一个副产品，我们给出了简单的描述Gorenstein三重奇点之间的过渡函数的两个坐标图的小分辨率。为了获得这些结果，我们开发的技术进行小的决议和小吹下来，包括一个算法吹下来的特殊$\PP^1$的。特别是，我们猜想，孤立Gorenstein三重奇点的小决议，可以通过变形矩阵分解简单的表面奇点-并证明这在长度1和长度2的情况下。
We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain Intriligator and Wecht's ADE classification of $\N=1$ superconformal theories which arise as RG fixed points of $\N = 1$ SQCD theories with adjoints. The connection between matrix models and $\N = 1$ gauge theories can be seen as evidence for the Dijkgraaf--Vafa conjecture. We find that ADE superpotentials in the Intriligator--Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yau's with corresponding ADE singularities. Moreover, in the additional $\Hat{O}, \Hat{A}, \Hat{D}$ and $\Hat{E}$ cases we find new singular geometries. These `hat' geometries are closely related to their ADE counterparts, but feature non-isolated singularities. As a byproduct, we give simple descriptions for small resolutions of Gorenstein threefold singularities in terms of transition functions between just two coordinate charts. To obtain these results we develop techniques for performing small resolutions and small blow-downs, including an algorithm for blowing down exceptional $\PP^1$'s. In particular, we conjecture that small resolutions for isolated Gorenstein threefold singularities can be obtained by deforming matrix factorizations for simple surface singularities -- and prove this in the length 1 and length 2 cases.
影响因子：
0.9
作者：
A. Duncan
通讯作者：
A. Duncan