标题： 质量变形ABJM理论在压扁球面上的精确大$N$展开 显示英文标题

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

摘要： 本文研究了质量形变ABJM理论在squashed三球面上的配分函数。特别是，我们将注意力集中在Chern-Simons水平为$\pm 1$的情形，并应用该理论与带有adjoint超多重态和fundamental超多重态的$\mathcal{N}=4$ $\mathrm{U}\left(N\right)$ 超Yang-Mills理论之间的对偶性。对于一个依赖于squashing参数的特殊质量参数，我们发现配分函数可以写成具有非平凡密度矩阵的理想费米气体的配分函数形式。通过研究这个密度矩阵，我们解析地推导出在$1/N$中配分函数的所有阶微扰展开式，结果发现其形式为Airy函数。我们的结果不仅与先前的研究发现和猜想一致，还导致了配分函数的整体常数因子的新公式。此外，我们还研究了$N$取小但有限值时配分函数的精确值。 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 $N$.