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arXiv 0911.4797hep-th
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Penner型矩阵模型与Seiberg-Witten理论

Penner Type Matrix Model and Seiberg-Witten Theory

Tohru Eguchi, Kazunobu Maruyoshi

备注：
22 pages; v2: references added, typos corrected; v3: a version to appear in JHEP
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摘要：

本文讨论了Dijkgraaf和Vafa最近提出的Penner型矩阵模型，利用矩阵模型与二维CFT的联系，对四维规范理论与Liouville理论之间的关系作了可能的解释。本文首先考虑N_f = 4，N = 2超对称规范理论的紫外区和红外区的规范耦合关系为$q_{\rm UV}={\vartheta_2(q_{\rm IR})^4/\vartheta_3(q_{\rm IR})^4}$。然后利用这个关系讨论了模变换对矩阵模型的作用，并确定了它的谱曲线。我们还讨论了N_f = 4矩阵模型中质量味的解耦问题，并导出了描述渐近自由N = 2规范理论的矩阵模型.我们发现Penner型矩阵理论正确地再现了N = 2超对称规范理论的标准结果。

英文摘要：

We discuss the Penner type matrix model recently proposed by Dijkgraaf and Vafa for a possible explanation of the relation between four-dimensional gauge theory and Liouville theory by making use of the connection of the matrix model to two-dimensional CFT. We first consider the relation of gauge couplings defined in UV and IR regimes of N_f = 4, N = 2 supersymmetric gauge theory being related as $q_{\rm UV}={\vartheta_2(q_{\rm IR})^4/\vartheta_3(q_{\rm IR})^4}$. We then use this relation to discuss the action of modular transformation on the matrix model and determine its spectral curve. We also discuss the decoupling of massive flavors from the N_f = 4 matrix model and derive matrix models describing asymptotically free N = 2 gauge theories. We find that the Penner type matrix theory reproduces correctly the standard results of N = 2 supersymmetric gauge theories.

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