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 ℙ3. At three loops, we obtain a K3 surface which arises as a branched surface over two genus-one curves in ℙ1 × ℙ1. 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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Vergu, C., Volk, M. Traintrack Calabi-Yaus from twistor geometry. J. High Energ. Phys. 2020, 160 (2020). https://doi.org/10.1007/JHEP07(2020)160
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DOI: https://doi.org/10.1007/JHEP07(2020)160