论文标题
颜色为颜色的广义双节标量振幅：本地平面性
Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity
论文作者
论文摘要
BIADJOINT标量理论具有立方相互作用，并且在$ {\ rm su}（n）\ times {\ rm su} \ big（{\ tilde n} \ big）$的$ {\ rm su}（n）\ times {\ rm su} \ big）的biadjoint表示中进行了转换。幅度是根据使用Feynman图计算出的部分幅度来分解的“颜色”，这些幅度是相对于两个订单的同时平面的。 2019年，引入了基于概括的Feynman图（GFD）的双节标量振幅的概括。 GFD是Feynman图的集合，该图是通过将“局部平面性”的其他约束结合到组合中的公制树木安排中的额外约束。在这项工作中，我们提出了对色顺序的自然概括，从而导致色彩幅度幅度。广义颜色排序（GCO）定义为标准颜色订购的集合，从$ \ mathbb {rp}^2 $上的投影线的布置中，这些颜色订购的集合是从精确意义上诱导的。我们介绍了$ n \ leq 9 $通用颜色订购和GFD的结果，在每种情况下都会发现新现象。我们发现了一般的解耦身份，并提出了“无色”广义标量振幅的定义。我们还为任意$ \ mathbb {rp}^{k-1} $提出了GCO的概念，讨论他们的一些属性，并对他们的GFD发表评论。在同伴论文中，我们使用CEGM积分公式探讨了部分振幅的定义。
The biadjoint scalar theory has cubic interactions and fields transforming in the biadjoint representation of ${\rm SU}(N)\times {\rm SU}\big({\tilde N}\big)$. Amplitudes are "color" decomposed in terms of partial amplitudes computed using Feynman diagrams which are simultaneously planar with respect to two orderings. In 2019, a generalization of biadjoint scalar amplitudes based on generalized Feynman diagrams (GFDs) was introduced. GFDs are collections of Feynman diagrams derived by incorporating an additional constraint of "local planarity" into the construction of the arrangements of metric trees in combinatorics. In this work, we propose a natural generalization of color orderings which leads to color-dressed amplitudes. A generalized color ordering (GCO) is defined as a collection of standard color orderings that is induced, in a precise sense, from an arrangement of projective lines on $\mathbb{RP}^2$. We present results for $n\leq 9$ generalized color orderings and GFDs, uncovering new phenomena in each case. We discover generalized decoupling identities and propose a definition of the "colorless" generalized scalar amplitude. We also propose a notion of GCOs for arbitrary $\mathbb{RP}^{k-1}$, discuss some of their properties, and comment on their GFDs. In a companion paper, we explore the definition of partial amplitudes using CEGM integral formulas.
