On geometry and matrix models
On geometry and matrix models
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关于几何和矩阵模型
DOI：
10.1016/s0550-3213(02)00764-2
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
C. Vafa
中科院分区：
文献类型：
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作者：
R. Dijkgraaf;C. Vafa
指出了矩阵模型、拓扑弦和N =1超对称规范理论之间关系的两个推广。首先，我们注意到，通过考虑酉矩阵模型的双标度极限，我们可以得到大N的局部卡-丘几何，工程师N =2规范理论。特别地，Gross-Witten单格元晶格模型的双标度极限给出了SU（2）Seiberg-Witten解，包括其诱导引力修正。其次，我们指出，N =1的ADE规范理论的有效超势项类似地计算的大N多矩阵模型，已被认为是在随机表面上的ADE最小模型的背景下。相关的谱曲线是作为配分函数的Virasoro和W-约束获得的多个分支覆盖。
We point out two extensions of the relation between matrix models, topological strings and N =1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large-N duals of the local Calabi–Yau geometries that engineer N =2 gauge theories. In particular, a double scaling limit of the Gross–Witten one-plaquette lattice model gives the SU(2) Seiberg–Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N =1 ADE quiver gauge theories is similarly computed by large-N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.