Phys.Rev.D, 112, 046023 (2025)
Exact large N expansion of N=4 circular quiver Chern-Simons theories
Naotaka Kubo1, Tomoki Nosaka2,* and Y.Pang1,3
1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.
2 Shanghai Institute for Mathematics and Interdisciplinary Sciences, Block A, International Innovation Plaza, No. 657 Songhu Road, Yangpu District, Shanghai, China.
3 Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China.
* nosaka@simis.cn
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.
