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Instanton counting with a surface operator and the chain-saw quiver

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Abstract

We describe the moduli space of SU(N) instantons in the presence of a general surface operator of type N = n 1 + ⋯ + n M in terms of the representations of the so-called chain-saw quiver, which allows us to write down the instanton partition function as a summation over the fixed point contributions labeled by Young diagrams. We find that the instanton partition function depends on the ordering of n I which fixes a choice of the parabolic structure. This is in accord with the fact that the Verma module of the W-algebra also depends on the ordering of n I . By explicit calculations, we check that the partition function agrees with the norm of a coherent state in the corresponding Verma module.

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Authors and Affiliations

  1. Graduate School of Mathematics and KMI, Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, 464-8602, Japan

    Hiroaki Kanno

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, 08504, U.S.A.

    Yuji Tachikawa

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  1. Hiroaki Kanno
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  2. Yuji Tachikawa
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Correspondence to Yuji Tachikawa.

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On leave from IPMU, the University of Tokyo.

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Kanno, H., Tachikawa, Y. Instanton counting with a surface operator and the chain-saw quiver. J. High Energ. Phys. 2011, 119 (2011). https://doi.org/10.1007/JHEP06(2011)119

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