标题： 显式大 $N$ 约翰内斯·冯·诺伊曼代数来自矩阵模型 显示英文标题

标题： Explicit large $N$ von Neumann algebras from matrix models

摘要： 我们构建了一个大的量子力学系统家族，在大$N$极限下，它们会产生一种涌现的 III 型$_1$范数代数。它们的划分函数是出现在各种规范理论研究中的矩阵积分。我们在这些系统中计算了实时、有限温度的相关函数，并表明在大$N$时它们由一种涌现的 III 型$_1$范数代数描述。该代数的基础谱密度以离散矩阵模型的特征值密度的闭合形式计算得出。此外，我们解释了如何系统地将这些理论提升为具有 Hagedorn 转变的系统，并表明只有在 Hagedorn 温度以上才会出现 III 型$_1$代数。最后，我们在例子中经验性地观察到量子力学的状态空间与卡勒-丘流形之间的对应关系。 显示英文摘要

摘要： We construct a large family of quantum mechanical systems that give rise to an emergent type III$_1$ von Neumann algebra in the large $N$ limit. Their partition functions are matrix integrals that appear in the study of various gauge theories. We calculate the real-time, finite temperature correlation functions in these systems and show that they are described by an emergent type III$_1$ von Neumann algebra at large $N$. The spectral density underlying this algebra is computed in closed form in terms of the eigenvalue density of a discrete matrix model. Furthermore, we explain how to systematically promote these theories to systems with a Hagedorn transition, and show that a type III$_1$ algebra only emerges above the Hagedorn temperature. Finally, we empirically observe in examples a correspondence between the space of states of the quantum mechanics and Calabi--Yau manifolds.