arXiv 0909.24532009-09-13hep-th

Toda理论、矩阵模型、拓扑弦和N=2规范系统

Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems

Robbert Dijkgraaf, Cumrun Vafa

备注：: 41 pages, 11 figures

摘要：

我们考虑黎曼曲面上具有A_{n-1}奇异性的IIB型几何的拓扑弦配分函数，包括Nekrasov变形。这些模型实现了Gaiotto及其合作者最近研究的N=2 SU（n）超共形规范系统。采用大N对偶，我们表明为什么在这些背景中的拓扑弦的配分函数被捕获的手征块的A_{n-1}户田系统，并推导出字典最近提出的Alday，Gaiotto和立川。对于亏格为零的黎曼曲面的情况下，我们展示了如何这些系统也可以实现彭纳式矩阵模型与对数电位。Seiberg-Witten曲线可以理解为这些矩阵模型的光谱曲线，其在大N处全息地出现。在这种情况下，Nekrasov变形映射到广义矩阵模型的β系综，这反过来又映射到具有一般背景电荷的户田系统。当n和N都很大时，我们还指出了这个系统的双全息的概念。

英文摘要：

We consider the topological string partition function, including the Nekrasov deformation, for type IIB geometries with an A_{n-1} singularity over a Riemann surface. These models realize the N=2 SU(n) superconformal gauge systems recently studied by Gaiotto and collaborators. Employing large N dualities we show why the partition function of topological strings in these backgrounds is captured by the chiral blocks of A_{n-1} Toda systems and derive the dictionary recently proposed by Alday, Gaiotto and Tachikawa. For the case of genus zero Riemann surfaces, we show how these systems can also be realized by Penner-like matrix models with logarithmic potentials. The Seiberg-Witten curve can be understood as the spectral curve of these matrix models which arises holographically at large N. In this context the Nekrasov deformation maps to the beta-ensemble of generalized matrix models, that in turn maps to the Toda system with general background charge. We also point out the notion of a double holography for this system, when both n and N are large.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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