论文标题
前进到adynkrafields：年轻的tableaux到10d的组件字段，n = 1标量超级场
Advening to Adynkrafields: Young Tableaux to Component Fields of the 10D, N = 1 Scalar Superfield
论文作者
论文摘要
从由Dynkin标签引用的节点构建的较高维敏捷开始，我们定义“ adynkras”。这些提出了一种计算直接的方式来描述所有超级空间中超级典型中包含的组件字段。我们明确讨论十个维度超级空间的案例。我们通过通过对年轻的Tableaux和Dynkin Labels的扩展来替换传统的$θ$扩展来表明这是可能的。无需引入$σ$ - amatrices，这允许从Adynkras $ \到$ Young Tableaux $ \ $ Young tableaux $ \ to $ compontion Field索引索引结构的快速段落，同时与使用超级领域的起点相比，同时提高了计算效率。为了实现我们的目标，这项工作引入了一种新的图形方法“绑定规则”，该方法提供了利特伍德（Littlewood）1950年数学结果的替代方法，该方法证明了使用特定的Schur功能系列的分支规则。这种推理线的最终点是基于年轻的tableaux的数学扩展的引入，并且在算法上优于超级场。扩展以“ adynkrafields”的名称结合在一起，因为它们结合了Adinkras和Dynkin标签的概念。
Starting from higher dimensional adinkras constructed with nodes referenced by Dynkin Labels, we define "adynkras." These suggest a computationally direct way to describe the component fields contained within supermultiplets in all superspaces. We explicitly discuss the cases of ten dimensional superspaces. We show this is possible by replacing conventional $θ$-expansions by expansions over Young Tableaux and component fields by Dynkin Labels. Without the need to introduce $σ$-matrices, this permits rapid passages from Adynkras $\to$ Young Tableaux $\to$ Component Field Index Structures for both bosonic and fermionic fields while increasing computational efficiency compared to the starting point that uses superfields. In order to reach our goal, this work introduces a new graphical method, "tying rules," that provides an alternative to Littlewood's 1950 mathematical results which proved branching rules result from using a specific Schur function series. The ultimate point of this line of reasoning is the introduction of mathematical expansions based on Young Tableaux and that are algorithmically superior to superfields. The expansions are given the name of "adynkrafields" as they combine the concepts of adinkras and Dynkin Labels.
