Traintrack Calabi-Yaus from twistor geometry
Cristian Vergu, Matthias Volk
Abstract
A bstract 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 ℙ 3 . At three loops, we obtain a K3 surface which arises as a branched surface over two genus-one curves in ℙ 1 × ℙ 1 . We present an analysis of its properties. We also discuss the geometry at higher loops and the supersymmetrization of the construction.
Topics & Concepts
Twistor theoryPhysicsSingularityLocus (genetics)GeometrySingularity theorySurface (topology)GenusIntersection (aeronautics)Gravitational singularityCubic surfaceIsolated singularityElliptic integralMathematical physicsAlgebraic geometryPlanarAlgebraic Geometry and Number TheoryGeometry and complex manifoldsBlack Holes and Theoretical Physics