JHEP, 02, 106 (2025)
Exact large N expansion of mass deformed ABJM theory on squashed sphere
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.
* naotaka.kubo@yukawa.kyoto-u.ac.jp
Abstract
In this paper we study the partition function of the mass deformed ABJM theory on a squashed three sphere. In particular, we focus on the case with the Chern-Simons levels being ±1 and apply a duality between this theory and the N = 4 U (N) super Yang-Mills theory with an adjoint hypermultiplet and a fundamental hypermultiplet. For a special mass parameter depending on the squashing parameter, we find that the partition function can be written as that of an ideal Fermi gas with a non-trivial density matrix. By studying this density matrix, we analytically derive the all order perturbative expansion of the partition function in 1/N, which turns out to take the form of the Airy function. Our results not only align with previous findings and conjectures but also lead to a new formula for the overall constant factor of the partition function. We also study the exact values of the partition function for small but finite values of N.
