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Seiberg-Witten theory, matrix model and AGT relation

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Abstract

We discuss the Penner-type matrix model which has been proposed to explain the AGT relation between the 2-dimensional Liouville theory and 4-dimensional \( \mathcal{N} = 2 \) superconformal gauge theories. In our previous communication we have obtained the spectral curve of the matrix model and showed that it agrees with that derived from M-theory. We have also discussed the decoupling limit of massive flavors and proposed new matrix models which describe Seiberg-Witten theory with flavors N f = 2, 3. In this article we explicitly evaluate the free energy of these matrix models and show that they in fact reproduce the amplitudes of Seiberg-Witten theory.

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Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan

    Tohru Eguchi & Kazunobu Maruyoshi

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  1. Tohru Eguchi
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  2. Kazunobu Maruyoshi
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Correspondence to Kazunobu Maruyoshi.

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Eguchi, T., Maruyoshi, K. Seiberg-Witten theory, matrix model and AGT relation. J. High Energ. Phys. 2010, 81 (2010). https://doi.org/10.1007/JHEP07(2010)081

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