发表机构
Université Paris-Saclay, CEA; Faculté des Sciences et Techniques (ICMPA-UNESCO Chair) Université d’Abomey-Calavi（巴黎萨克雷大学，法国原子能和替代能源委员会; 阿博米-卡拉维大学科学与技术学院（ICMPA-教科文组织讲席））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于部分矩阵值中间场的关系背景场方法，为随机矩阵模型构建保持对称性的重整化群流，在大N极限下实现自洽背景场，并发现红外理论具有与双标度指数精确匹配的临界指数。
AI 中文摘要
为离散引力模型构建一个可靠的重整化群（RG）流，并保持其底层对称群（通常为$U(N)$或$O(N)$）不变，仍然是一个未解决的问题。对于本文所关注的随机矩阵模型，该对称性本质上与编码二维量子欧几里得时空随机几何的相互作用相关联。我们发展了一种基于引入部分矩阵值中间场的新方法。在大$N$极限下，测度集中效应强烈抑制其奇异值的涨落，使其能够扮演自洽背景场的角色。这为关系型RG提供了基础，其中尺度的概念由中间场对角化的基中的有效高斯测度动态诱导。我们的构造保持了原始模型的对称性，并允许定义良好的连续极限。我们证明了所得的红外理论由一个三维非局域欧几里得场论描述，该场论具有非平凡的类Wilson-Fisher不动点和单一相关方向。值得注意的是，相关的临界指数恰好与标准双标度指数匹配。最后，我们讨论了背景场方法向其他离散引力模型（如随机张量模型）和不同对称群的扩展，以及与更形式化的RG框架和信息几何的联系。
英文摘要
The construction of a reliable renormalization group (RG) flow for discrete gravity models that preserves their underlying symmetry group, typically $U(N)$ or $O(N)$, remains an open problem. For random matrix models, which are the focus of this paper, this symmetry is intrinsically tied to the interactions encoding the random geometry of two-dimensional quantum Euclidean spacetime. We develop a novel approach based on the introduction of a partial matrix-valued intermediate field. In the large-$N$ limit, measure concentration strongly suppresses fluctuations of its singular values, allowing it to play the role of a self-consistent background field. This provides the basis for a relational RG in which the notion of scale is dynamically induced by the effective Gaussian measure in the basis where the intermediate field is diagonal. Our construction preserves the symmetry of the original model and admits a well-defined continuum limit. We show that the resulting infrared theory is described by a three-dimensional non-local Euclidean field theory with a non-trivial Wilson-Fisher-like fixed point and a single relevant direction. Remarkably, the associated critical exponent exactly matches the standard double-scaling exponent. We finally discuss extensions of the background-field approach to other discrete gravity models, such as random tensor models, and to different symmetry groups, as well as connections with more formal RG frameworks and information geometry.
Comments64 pages, 16 figures
