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The three-dimensional \( \mathcal{N} \) = 2 superfishnet theory

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  • Published: 21 January 2025
  • Volume 2025, article number 100, (2025)
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The three-dimensional \( \mathcal{N} \) = 2 superfishnet theory
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  • Moritz Kade  ORCID: orcid.org/0000-0003-0912-50051 

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A preprint version of the article is available at arXiv.

Abstract

We propose a double-scaling limit of β-deformed ABJM theory in three-dimensional \( \mathcal{N} \) = 2 superspace, and a non-local deformation thereof. Due to the regular appearance of the theory’s Feynman supergraphs, we refer to this superconformal and integrable theory as the superfishnet theory. We use techniques inspired by the integrability of bi-scalar fishnet theory and adapted to superspace to calculate the zero-mode-fixed thermodynamic free energy, the corresponding critical coupling, and the exact all-loop scaling dimensions of various operators. Furthermore, we confirm the results of the supersymmetric dynamical fishnet theory by applying our methods to four-dimensional \( \mathcal{N} \) = 1 superspace.

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Acknowledgments

The author is grateful for the support, collaboration and many discussions with Matthias Staudacher. Furthermore, the author would like to thank Changrim Ahn for collaboration and discussing related subjects. The author is thankful to have benefited from discussions with Changrim Ahn, Gwenaël Ferrando, Nikolay Gromov, Vladimir Kazakov, Enrico Olivucci, Giulia Peveri, Lorenzo Di Pietro and Matthias Staudacher. Special thanks to Matthias Staudacher and Changrim Ahn for very careful readings of the manuskript. This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Projektnummer 417533893/GRK2575 “Rethinking Quantum Field Theory”.

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  1. Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, Zum Großen Windkanal 2, 12489, Berlin, Germany

    Moritz Kade

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Cite this article

Kade, M. The three-dimensional \( \mathcal{N} \) = 2 superfishnet theory. J. High Energ. Phys. 2025, 100 (2025). https://doi.org/10.1007/JHEP01(2025)100

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  • Received: 30 October 2024

  • Accepted: 08 December 2024

  • Published: 21 January 2025

  • DOI: https://doi.org/10.1007/JHEP01(2025)100

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Keywords

  • Integrable Field Theories
  • Superspaces
  • Lattice Integrable Models
  • Chern-Simons Theories
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