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Penner type matrix model and Seiberg-Witten theory

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Abstract

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, \( \mathcal{N} \) = 2 supersymmetric gauge theory being related as q UV = ϑ2(q IR)4/ϑ3(q 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 \( \mathcal{N} \) = 2 gauge theories. We find that the Penner type matrix theory reproduces correctly the standard results of \( \mathcal{N} \) = 2 supersymmetric gauge theories.

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  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

    Tohru Eguchi & Kazunobu Maruyoshi

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  1. Tohru Eguchi
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Correspondence to Tohru Eguchi.

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Eguchi, T., Maruyoshi, K. Penner type matrix model and Seiberg-Witten theory. J. High Energ. Phys. 2010, 22 (2010). https://doi.org/10.1007/JHEP02(2010)022

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