论文标题
Feynman积分的集群代数
Cluster algebras for Feynman integrals
论文作者
论文摘要
我们在Feynman积分中启动群集代数的研究。我们提供的证据表明，四点Feynman积分具有一个脱壳腿，由$ c_ {2} $ cluster代数描述，我们发现限制允许功能空间的群集邻接关系。通过将$ c_ {2} $嵌入$ a_3 $ cluster代数内，我们可以通过扩展的steinmann关系来识别这些邻接的六颗粒无质量散射。我们发现群集代数连接限制了向量玻色子或希格斯和喷气幅度的功能空间，并且对于最近在$ \ Mathcal {n} = 4 $ super yang-yang-mills中考虑的形式因素。我们解释了一般的程序，用于研究广义性聚类函数和群集代数的字母之间的关系，并使用它们来提供具有群集代数的一环字母的各种识别。特别是，我们展示了如何从最近讨论的与$ g（4,8）$ cluster代数相关的双重共形八粒子字母中获得五粒子散射的单环字母。
We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a $C_{2}$ cluster algebra, and we find cluster adjacency relations that restrict the allowed function space. By embedding $C_{2}$ inside the $A_3$ cluster algebra, we identify these adjacencies with the extended Steinmann relations for six-particle massless scattering. The cluster algebra connection we find restricts the functions space for vector boson or Higgs plus jet amplitudes, and for form factors recently considered in $\mathcal{N}=4$ super Yang-Mills. We explain general procedures for studying relationships between alphabets of generalized polylogarithmic functions and cluster algebras, and use them to provide various identifications of one-loop alphabets with cluster algebras. In particular, we show how one can obtain one-loop alphabets for five-particle scattering from a recently discussed dual conformal eight-particle alphabet related to the $G(4,8)$ cluster algebra.
