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  • Open Access

Exact large N expansion of N=4 circular quiver Chern-Simons theories

Naotaka Kubo1,*, Tomoki Nosaka2,3,†, and Yi Pang1,4,‡

  • *Contact author: naotaka.kubo@yukawa.kyoto.u-ac.jp
  • †Contact author: nosaka@simis.cn
  • ‡Contact author: pangyi1@tju.edu.cn
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Phys. Rev. D 112, 046023 – Published 28 August, 2025

DOI: https://doi.org/10.1103/x5h6-r3dd

Abstract

In this work, we revisit the exact computation of the round sphere partition function of 3d N=4 circular quiver Chern-Simons theories with mass and Fayet-Iliopoulos (FI) deformations. Utilizing the Fermi gas formalism, we derive the large N expansion of the partition function and determine the Airy function structure, parametrized by three functions C, B, and A. We propose a novel closed-form expression for A that incorporates the effects of FI parameters and satisfies various consistency constraints from quiver reductions. As an application, by using an accidental coincidence of the Fermi gas density matrices we extend our results to the squashed sphere partition function of N=4 super Yang-Mills theories with an adjoint hypermultiplet and multiple fundamental hypermultiplets. Our findings provide further evidence for the universality of the Airy function structure in supersymmetric gauge theories of multiple M2-branes.

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Outline

Information

Phys. Rev. D 112, 046023– Published 28 August, 2025
  • Received 14 June 2025
  • Accepted 28 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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