Abstract
We construct the Fermi gas formalism for the partition function of supersymmetric Chern-Simons theories with affine D-type quiver diagrams with non-uniform ranks of the gauge groups and Fayet-Illiopoulos parameters by two different approaches: the open string formalism and the closed string formalism. In the closed string formalism approach, we find a novel connection between the partition function of this theory and the partition function of a four-nodes circular quiver supersymmetric Chern-Simons theory. We also studied a symmetry of a density matrix appeared in the closed string formalism. We further calculate the exact values of the partition function for finite N, with which we identified the exponent of the leading non-perturbative effect in 1/N corresponding to the worldsheet instantons in the circular quiver supersymmetric Chern-Simons theories.
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Acknowledgments
The authors thank Giulio Bonelli, Fran Globlek and Alessandro Tanzini for the collaboration during the early stages of the project. We are also grateful to Sanefumi Moriyama for valuable discussion. Preliminary results of this paper were presented by NK in a international school “The 18th Kavli Asian Winter School on Strings, Particles and Cosmology” at Yukawa Institute for Theoretical Physics, Kyoto University. Part of the results in appendix D was computed by using the high performance computing facility provided by Yukawa Institute for Theoretical Physics (Sushiki server). The research activity of NK is partially supported by National key research and development program under grand No. 2022YFE0134300.
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Kubo, N., Nosaka, T. Fermi gas formalism for D-type quiver Chern-Simons theory with non-uniform ranks. J. High Energ. Phys. 2024, 79 (2024). https://doi.org/10.1007/JHEP07(2024)079
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DOI: https://doi.org/10.1007/JHEP07(2024)079