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\( {{\mathcal{W}}_3} \) irregular states and isolated \( \mathcal{N}=2 \) superconformal field theories

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Abstract

We explore the proposal that the six-dimensional (2, 0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated \( \mathcal{N}=2 \) superconformal theories of Argyres-Douglas type, and to two-dimensional conformal field theory with irregular states. Following the approach of Gaiotto-Teschner for the Virasoro case, we construct \( {{\mathcal{W}}_3} \) irregular states by colliding a single SU(3) puncture with several regular punctures of simple type. If n simple punctures are colliding with the SU(3) puncture, the resulting irregular state is a simultaneous eigenvector of the positive modes L n , . . . , L 2n and W 2n , . . . , W 3n of the \( {{\mathcal{W}}_3} \) algebra. We find the corresponding isolated SCFT with an SU(3) flavor symmetry as a nontrivial IR fixed point on the Coulomb branch of the SU(3) linear quiver gauge theories, by confirming that its Seiberg-Witten curve correctly predicts the conditions for the \( {{\mathcal{W}}_3} \) irregular states. We also compare these SCFT’s with the ones obtained from the BPS quiver method.

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Authors and Affiliations

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

    Hiroaki Kanno

  2. California Institute of Technology, 452-48, Pasadena, California, 91125, U.S.A.

    Kazunobu Maruyoshi

  3. High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan

    Shotaro Shiba

  4. Mathematical Physics Lab., RIKEN Nishina Center, Saitama, 351-0198, Japan

    Masato Taki

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  1. Hiroaki Kanno
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  2. Kazunobu Maruyoshi
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  3. Shotaro Shiba
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Correspondence to Shotaro Shiba.

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ArXiv ePrint: 1301.0721

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Kanno, H., Maruyoshi, K., Shiba, S. et al. \( {{\mathcal{W}}_3} \) irregular states and isolated \( \mathcal{N}=2 \) superconformal field theories. J. High Energ. Phys. 2013, 147 (2013). https://doi.org/10.1007/JHEP03(2013)147

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