标题： 质量变形ABJM理论在挤压球面上的精确大$N$展开 显示英文标题

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

摘要： 在本文中，我们研究了在挤压三维球面上质量变形的ABJM理论的分划函数。 特别是，我们关注CS层为$\pm 1$的情况，并应用该理论与带有伴随超多重态和基本超多重态的$\mathcal{N}=4$ $\mathrm{U}\left(N\right)$ 超杨-米尔斯理论之间的对偶性。 对于一个依赖于挤压参数的特殊质量参数，我们发现分划函数可以写成具有非平凡密度矩阵的理想费米气体的形式。 通过研究这个密度矩阵，我们解析地推导出分划函数在$1/N$中的所有阶次微扰展开，结果表明其形式为艾里函数。 我们的结果不仅与之前的发现和猜想一致，还导致了分划函数整体常数因子的新公式。 我们还研究了$N$取小但有限值时分划函数的精确值。 显示英文摘要

摘要： 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 $N$.