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M5-branes, toric diagrams and gauge theory duality

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Abstract

In this article we explore the duality between the low energy effective theory of five-dimensional \( \mathcal{N} = {1}\,{\text{SU}}{(N)^{{M - {1}}}} \) and SU(M)N−1 linear quiver gauge theories compactified on S 1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.

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Authors and Affiliations

  1. Fundamental Physics, Chalmers University of Technology, 41296, Göteborg, Sweden

    Ling Bao

  2. Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489, Berlin, Germany

    Elli Pomoni

  3. Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-Cho, Sakyo-Ku, Kyoto, Japan

    Masato Taki

  4. International School of Advanced Studies (SISSA), and INFN, Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy

    Futoshi Yagi

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  1. Ling Bao
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  2. Elli Pomoni
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  3. Masato Taki
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  4. Futoshi Yagi
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Correspondence to Elli Pomoni.

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ArXiv ePrint: 1112.5228

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Bao, L., Pomoni, E., Taki, M. et al. M5-branes, toric diagrams and gauge theory duality. J. High Energ. Phys. 2012, 105 (2012). https://doi.org/10.1007/JHEP04(2012)105

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