论文标题
孙子不变的信的注释
A Note on Letters of Yangian Invariants
论文作者
论文摘要
通过在平面$ {\ cal n}中重新定义扬式的不变式= 4 $ sym作为$ d \ log $ sym in Momentum-Twistor Space上的$ d \ log $表单，我们提出了一个纯粹的代数问题，即确定$ d \ log $ $ $ d \ log $的参数，我们称之为“字母”，对于任何Yangian Invariant。这些是动量扭曲器$ z $的函数，由矩阵$ c（α）$的参数化的正坐标给出，并根据多项式方程$ c（α）\ cdot z = 0 $进行了评估。我们提供的证据表明，扬式不变的字母与Grassmannian $ g（4，n）$的集群代数有关，这与$ n $ n $ point散射幅度的符号字母有关。对于$ n = 6,7 $，所有Yangian不变的字母收集包含$ g（4，n）$的群集$ {\ cal a} $坐标。我们确定与任何“四个质量”框相关的桑ian不变的代数字母，该框以$ n = 8 $重现了最近针对两循环振幅发现的$ 18 $乘型独立的代数符号字母。
Motivated by reformulating Yangian invariants in planar ${\cal N}=4$ SYM directly as $d\log$ forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of the $d\log$'s, which we call "letters", for any Yangian invariant. These are functions of momentum twistors $Z$'s, given by the positive coordinates $α$'s of parametrizations of the matrix $C(α)$, evaluated on the support of polynomial equations $C(α) \cdot Z=0$. We provide evidence that the letters of Yangian invariants are related to the cluster algebra of Grassmannian $G(4,n)$, which is relevant for the symbol alphabet of $n$-point scattering amplitudes. For $n=6,7$, the collection of letters for all Yangian invariants contains the cluster ${\cal A}$ coordinates of $G(4,n)$. We determine algebraic letters of Yangian invariant associated with any "four-mass" box, which for $n=8$ reproduce the $18$ multiplicative-independent, algebraic symbol letters discovered recently for two-loop amplitudes.
