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arXiv · 2411.07334

Exact large $N$ expansion of mass deformed ABJM theory on squashed sphere

Naotaka Kubo·Tomoki Nosaka·Yi Pang
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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 $\pm 1$ and apply a duality between this theory and the $\mathcal{N}=4$ $\mathrm{U}\left(N\right)$ 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 $N$.

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Naotaka Kubo, Tomoki Nosaka, Yi Pang. 2024-11-11. Exact large $N$ expansion of mass deformed ABJM theory on squashed sphere. https://arxiv.org/abs/2411.07334

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