论文标题
Twistor几何形状的Traintrack Calabi-Yaus
Traintrack Calabi-Yaus from Twistor Geometry
论文作者
论文摘要
我们直接在动量扭曲器空间中直接描述了Traintrack积分家族的主要奇点基因座的几何形状。对于两循环的情况（称为椭圆双重框），领先的奇点基因座是一条属的曲线，我们将其作为$ \ Mathbb {p}^{3} $的两个四边形的相交。在三个环上，我们获得了一个K3表面，该表面在$ \ Mathbb {p}^{1} \ times \ times \ mathbb {p}^{1} $中以两个属的曲线为单属曲线出现。我们对其性质进行了分析。我们还讨论了较高回路的几何形状以及结构的过度对称。
We describe the geometry of the leading singularity locus of the traintrack integral family directly in momentum twistor space. For the two-loop case, known as the elliptic double box, the leading singularity locus is a genus one curve, which we obtain as an intersection of two quadrics in $\mathbb{P}^{3}$. At three loops, we obtain a K3 surface which arises as a branched surface over two genus-one curves in $\mathbb{P}^{1} \times \mathbb{P}^{1}$. We present an analysis of its properties. We also discuss the geometry at higher loops and the supersymmetrization of the construction.
