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arXiv · 2005.08771

Traintrack Calabi-Yaus from Twistor Geometry

Cristian Vergu·Matthias Volk
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Abstract

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.

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Cristian Vergu, Matthias Volk. 2020-05-18. Traintrack Calabi-Yaus from Twistor Geometry. https://doi.org/10.1007/jhep07(2020)160

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