标题： SU(4)杨-米尔斯理论中中心环状物质的结构 显示英文标题

标题： Structure of center vortex matter in SU(4) Yang-Mills theory

摘要： 中心环结构在SU(4)杨-米尔斯理论中首次被研究，以阐明基本（中心电荷$\pm 1$）和双电荷环之间的相互作用。 与SU(3)不同，在SU(3)中电荷$+2$的环只是时空方向相反的基本环，而在SU(4)中这些可能性在物理上是不同的。 三维切片中的环结构可视化揭示了双电荷物体的各种表现方式，或是基本环的汇聚和匹配，或是孤立的双电荷环。 描述了一种算法，将每个双电荷链分类为这三种类型之一。 考虑了一组环统计数据，以量化环结构。 其中许多涉及新型的双电荷物体，包括它们的相对比例和链长，这些被分析以突出每种链类型的差异。 采用三种不同的格点间距来研究连续极限的接近情况。 发现环匹配链平均更短但出现频率更高，这归因于它们作为扩展中心单极子的解释。 此外，观察到环汇聚和环匹配的长度都遵循指数分布，从而可以引入一个常数概率，即双电荷链在传播过程中分裂为两个基本环的概率。 综合这些发现，提供了对SU(4)杨-米尔斯理论中构成中心环结构的环的特征描述。 显示英文摘要

摘要： The structure of center vortices is studied in SU(4) Yang-Mills theory for the first time to illuminate the interplay between elementary (center charge $\pm 1$) and doubly charged vortices. Unlike in SU(3), where charge $+2$ vortices are simply elementary vortices with reversed orientations in spacetime, these possibilities are physically distinct in SU(4). Visualizations of the vortex structure in three-dimensional slices reveal the various ways in which doubly charged objects manifest, as the convergence and matching of elementary vortices or as isolated doubly charged loops. An algorithm is described to classify every doubly charged chain as one of these three types. A collection of vortex statistics is considered to quantify the vortex structure. Many of these pertain to the novel doubly charged objects, including their relative proportions and chain lengths, which are analyzed to highlight the differences between each chain type. Three different lattice spacings are employed to investigate the approach to the continuum limit. Vortex matching chains are found to be shorter on average but also more prevalent than vortex convergences, ascribed to their interpretation as extended center monopoles. In addition, the lengths of both vortex convergences and vortex matchings are observed to follow an exponential distribution, allowing the introduction of a constant probability for a doubly charged chain to split into two elementary vortices as it propagates. Combined, these findings provide a characterization of the vortices that comprise center vortex structures in SU(4) Yang-Mills theory.