arXiv 1104.23862011-04-13hep-th

最简单的规范弦对偶是什么？

What is the Simplest Gauge-String Duality?

Rajesh Gopakumar

备注：: 30+1 pages, 6 figures

摘要：

我们提出了一个建议的字符串对偶最简单的大$N$理论，高斯矩阵积分的'tHooft限制，以及如何出现这种双重描述双线图。这是规范弦对偶的一般方法的具体实现，它将世界面黎曼面与大N规范理论的费曼-特胡夫图联系起来。我们表明，这种连接的一个特定版本（由Razamat提出），涉及整数Strebel微分，自然地解释了高斯矩阵的组合。我们发现，该算子可以明确地实现为一类特殊的全纯映射（Belyi映射）从世界表到{ \it目标空间} ${\mathbb P}^1$的和。我们被引导来识别这个目标空间与黎曼面相关的矩阵模型的（特征值）。在这个过程中，一个AdS/CFT一样的字典，为任意的单迹算子，也出现了全纯映射的字符串Witten图的作用。最后，我们提供了一些证据，证明上述弦对偶是${\mathbb P}^1$上的传统A-模型拓扑弦论。

英文摘要：

We make a proposal for the string dual to the simplest large $N$ theory, the Gaussian matrix integral in the 'tHooft limit, and how this dual description emerges from double line graphs. This is a specific realisation of the general approach to gauge-string duality which associates worldsheet riemann surfaces to the Feynman-'tHooft diagrams of a large N gauge theory. We show that a particular version (proposed by Razamat) of this connection, involving integer Strebel differentials, naturally explains the combinatorics of Gaussian matrix correlators. We find that the correlators can be explicitly realised as a sum over a special class of holomorphic maps (Belyi maps) from the worldsheet to a {\it target space} ${\mathbb P}^1$. We are led to identify this target space with the riemann surface associated with the (eigenvalues of the) matrix model. In the process, an AdS/CFT like dictionary, for arbitrary correlators of single trace operators, also emerges in which the holomorphic maps play the role of stringy Witten diagrams. Finally, we provide some evidence that the above string dual is the conventional A-model topological string theory on ${\mathbb P}^1$.

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