论文标题
协变颜色二元性二元性,霍普夫代数和渗透
Covariant color-kinematics duality, Hopf algebras and permutohedra
论文作者
论文摘要
基于颜色界面二元性,我们研究了其在YANG-MILLS-SCALAR(YMS)理论中的伯尔尼 - 卡拉斯科 - 约翰逊(BCJ)分子的组合结构和代数结构。 YMS振幅的BCJ分子的闭合形式和Pure-Yang-Mills(YM)的封闭形式表现出不错的准式Hopf hopf代数结构,有趣的是,它们可以被视为对组合置换式螺旋体的所有维度的总结。特别是,具有两个标量和$ n { - } 2 $ gluons的分子包含fubini编号($ f_ {n { - } 2} $),以一对一的通信为$(n { - } 3)$ - 尺寸 - 尺寸的domensiention commensional docementions undermiant and spurious-pole-poser(nunizatient-Pole-poper)的术语(n { - } 3)$ - 动量)。从这样的Hopf代数或置换体结构中,我们得出了分子的新递归关系,并在恒定体的每个伪极/方面进行了“分解”。一般的YMNENERATOR和PURE-EMS的结果相似。最后,有了特殊的参考力量选择,我们的结果暗示了具有两个巨大颗粒和$ n { - } 2 $ gluons/gravitons的重质量有效野外理论中的BCJ分子:我们观察到了重型限制的高度非平凡的取消,从而导致了在最近的工作中获得新的有效分子的新公式。
Based on the covariant color-kinematics duality, we investigate combinatorial and algebraic structures underlying their Bern-Carrasco-Johansson (BCJ) numerators of tree-level amplitudes in Yang-Mills-scalar (YMS) theory. The closed-formulae for BCJ numerators of YMS amplitudes and the pure-Yang-Mills (YM) ones exhibit nice quasi-shuffle Hopf algebra structures, and interestingly they can be viewed as summing over boundaries of all dimensions of a combinatorial permutohedron. In particular, the numerator with two scalars and $n{-}2$ gluons contains Fubini number ( $F_{n{-}2}$ ) of terms in one-to-one correspondence with boundaries of a $(n{-}3)$-dimensional permutohedron, and each of them has its own spurious-pole structures and a gauge-invariant numerator (both depending on reference momenta). From such Hopf algebra or permutohedron structure, we derive new recursion relations for the numerators and intriguing "factorization" on each spurious pole/facet of the permutohedron. Similar results hold for general YMS numerators and the pure-YM ones. Finally, with a special choice of reference momenta, our results imply BCJ numerators in a heavy-mass effective field theory with two massive particles and $n{-}2$ gluons/gravitons: we observe highly nontrivial cancellations in the heavy-mass limit, leading to new formulae for the effective numerators which resemble those obtained in recent works.