发表机构
National Institute of Technology, Akashi College; Keio University（国立高等专门学校明石工业高等専門学校; 庆应义塾大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从部分退禁闭视角研究热矩阵模型中的主导杨图，提出定义方案，并通过解析鞍点分析推导其形状与特征值分布的关系，揭示行数对应退禁闭子扇区大小。
AI 中文摘要
我们从部分退禁闭的视角，讨论了具有规范对称性的热矩阵模型中的主导表示（或杨图）。我们提出了一种为具有相互作用项的热矩阵模型定义主导表示的方案。作为一个具体例子，我们考虑了$N$很大的高斯矩阵模型。我们通过一种新的解析鞍点分析，基于U($\infty$)表示论到二维时空自由费米子的映射，获得了主导杨图的VKLS形状。这一计算直接推导了先前观察到的主导杨图形状与热和乐特征值分布之间的函数关系：复鞍点的位置自然地等同于特征值。主导杨图在部分退禁闭方面具有自然的解释：主导杨图的行数对应于退禁闭子扇区子矩阵的大小。
英文摘要
We discuss dominant representations (or Young diagrams), in thermal matrix models with gauge symmetry from the perspective of partial deconfinement. We propose a prescription for defining the dominant representations for thermal matrix models with interaction terms. As an explicit example, we consider the large-$N$ Gaussian matrix model. We obtain the Vershik--Kerov--Logan--Shepp (VKLS) shape of the dominant Young diagrams through a new analytic saddle-point analysis based on a mapping of the representation theory of U($\infty$) to free fermions in two spacetime dimensions. This computation provides a direct derivation of the previously observed functional relation between the shape of the dominant Young diagrams and the eigenvalue distribution of the thermal holonomy: the position of the complex saddle point is naturally identified with the eigenvalue. The dominant Young diagrams admit a natural interpretation in terms of partial deconfinement: the number of rows in the dominant Young diagrams matches the size of the submatrix corresponding to the deconfined subsector.
Comments1+49 pages, 4 figures. v2: References added; minor corrections
