论文标题
统一矩阵模型，自由费米昂合奏和巨型重力扩展
Unitary matrix models, free fermion ensembles, and the giant graviton expansion
论文作者
论文摘要
我们考虑了一类矩阵积分$ u（n）$上的矩阵积分，其中包含一组无限的耦合，其特征是$ f（q）= \ sum_ {n \ ge 1} a_n q^n $，带有$ a_n \ in \ mathbb {z} $。这种积分在物理学中出现，作为在$ s^3 $上的自由四维规定理论的分区函数，尤其是作为超级阳米尔斯理论的超符号索引。我们表明，任何此类模型都可以用无限耦合集合的集合中的自由费米子系统表示。在给定的量子状态中集成费米子会导致收敛的扩展作为一系列决定因素，如多年前Borodin-Okounkov所示。通过进一步平均合奏，我们获得了矩阵积分的公式，作为$ q $ series，其连续术语被$ q^{αn +β} $抑制的术语，其中$α$，$β$不取决于$ n $。这为巨型重力扩张提供了矩阵模型的解释，该解释是最近在文献中观察到的。
We consider a class of matrix integrals over the unitary group $U(N)$ with an infinite set of couplings characterized by a series $f(q)=\sum_{n \ge 1} a_n q^n$, with $a_n \in \mathbb{Z}$. Such integrals arise in physics as the partition functions of free four-dimensional gauge theories on $S^3$ and, in particular, as the superconformal index of super Yang-Mills theory. We show that any such model can be expressed in terms of a system of free fermions in an ensemble parameterized by the infinite set of couplings. Integrating out the fermions in a given quantum state leads to a convergent expansion as a series of determinants, as shown by Borodin-Okounkov many years ago. By further averaging over the ensemble, we obtain a formula for the matrix integral as a $q$-series with successive terms suppressed by $q^{αN + β}$ where $α$, $β$ do not depend on $N$. This provides a matrix-model explanation of the giant graviton expansion that has been observed recently in the literature.
