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arXiv 0810.4944hep-th
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Seiberg-Witten理论与矩阵模型

Seiberg-Witten theory and matrix models

Albrecht Klemm, Piotr Sułkowski

备注：
43 pages, 5 figures; typos corrected, references added, derivation of the curve in section 4.2 corrected; published version
发表信息：
Nucl.Phys.B819:400-430,2009
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摘要：

我们推导出一个家庭的矩阵模型编码的解决方案，在4和5维的Seiberg-Witten理论。这些矩阵模型的配分函数等于相应的Nekrasov配分函数，其谱曲线是相应理论的Seiberg-Witten曲线。在几何工程的结果中，5维情形提供了一个新的矩阵模型表述的拓扑弦论上的广泛的非紧复曲面的Calabi-Yau流形。这种方法还统一和推广了其他矩阵模型，如Eguchi-Yang矩阵模型，$P^1$上丛的矩阵模型，透镜空间的Chern-Simons矩阵模型，这些模型是由于我们的一般结果的各种限制而产生的。

英文摘要：

We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves are the Seiberg-Witten curves of the corresponding theories. In consequence of the geometric engineering, the 5-dimensional case provides a novel matrix model formulation of the topological string theory on a wide class of non-compact toric Calabi-Yau manifolds. This approach also unifies and generalizes other matrix models, such as the Eguchi-Yang matrix model, matrix models for bundles over $P^1$, and Chern-Simons matrix models for lens spaces, which arise as various limits of our general result.

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