Traintrack Calabi-Yaus from twistor geometry. (English) Zbl 1451.81362
Summary: 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.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 14J28 | \(K3\) surfaces and Enriques surfaces |
Software:
PALPReferences:
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