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Five-dimensional AGT conjecture and the deformed Virasoro algebra

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Abstract

We study an analog of the AGT (Alday-Gaiotto-Tachikawa) relation in five dimensions. We conjecture that the instanton partition function of 5D \( \mathcal{N} = 1 \) pure SU(2) gauge theory coincides with the inner product of the Gaiotto-like state in the deformed Virasoro algebra. In four-dimensional case, a relation between the Gaiotto construction and the theory of Braverman and Etingof is also discussed.

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Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Hidetoshi Awata

  2. Department of Mathematics, Faculty of Science, Kobe University, Hyogo, 657-8501, Japan

    Yasuhiko Yamada

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  1. Hidetoshi Awata
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  2. Yasuhiko Yamada
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Correspondence to Hidetoshi Awata.

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ArXiv ePrint: 0910.4431

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Awata, H., Yamada, Y. Five-dimensional AGT conjecture and the deformed Virasoro algebra. J. High Energ. Phys. 2010, 125 (2010). https://doi.org/10.1007/JHEP01(2010)125

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