论文标题
Feynman积分的符号学来自Twistor几何形状
The symbology of Feynman integrals from twistor geometries
论文作者
论文摘要
我们通过在动量扭曲器空间中考虑对应于其领先奇点(LS)的动量扭曲空间中的几何配置来研究平面Feynman积分的符号学。在动量扭曲器空间中切割传播器等于与循环和外部双重动量相关的相交线,包括与Infinity点相关的特殊线,这打破了双形状对称性。我们表明,这些线路上的交叉点的交叉比例,尤其是在无限线上的那些线,自然会在$ d =4-2ε$中为feynman积分产生符号字母,其中包括并推广其LS。在一个循环中,我们使用从四核切割的相交点获得所有符号字母,直到五角大学运动学具有两个巨大的角落,它们与规范的微分方程(CDE)结果完全一致。然后,我们通过考虑更多由两环切口引起的交叉点来获得所有最多四个质量盒和一质量五角大楼运动学的双循环字母。最后,我们评论了群集代数如何从这种构建中出现,重要的是我们如何将方法扩展到非平面积分。
We study the symbology of planar Feynman integrals in dimensional regularization by considering geometric configurations in momentum twistor space corresponding to their leading singularities (LS). Cutting propagators in momentum twistor space amounts to intersecting lines associated with loop and external dual momenta, including the special line associated with the point at infinity, which breaks dual conformal symmetry. We show that cross-ratios of intersection points on these lines, especially those on the infinity line, naturally produce symbol letters for Feynman integrals in $D=4-2ε$, which include and generalize their LS. At one loop, we obtain all symbol letters using intersection points from quadruple cuts for integrals up to pentagon kinematics with two massive corners, which agree perfectly with canonical differential equation (CDE) results. We then obtain all two-loop letters, for up to four-mass box and one-mass pentagon kinematics, by considering more intersections arising from two-loop cuts. Finally we comment on how cluster algebras appear from this construction, and importantly how we may extend the method to non-planar integrals.