1999/03/31 by Bjorn Andreas, BJÖRN ANDREAS, Gottfried Curio +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Bundle #Cover (algebra) #Fiber bundle #Fibered knot #Fibration #Geometry and complex manifolds #Gravitational singularity #Section (typography) #Standard Model (mathematical formulation) #hep-th
paper · pdf · doi:10.1142/s0217751x04018087
published as Int.J.Mod.Phys.A19:1987,2004 · 31 pages, 1 eps-figure, reference added, bundle parameters for dP9 model changed
openalex publication_date 2004/05/10 · arxiv created 2004/12/15 · arxiv updated 2014/11/17 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
We show that it is possible to construct supersymmetric three-generation models with the Standard Model gauge group in the framework of non-simply-connected elliptically fibered Calabi–Yau threefolds, without section but with a bi-section. The fibrations on a cover Calabi–Yau threefold, where the model has six generations of SU(5) and the bundle is given via the spectral cover description, use a different description of the elliptic fiber which leads to more than one global section. We present two examples of a possible cover Calabi–Yau threefold with a free involution: one is a fiber product of rational elliptic surfaces dP 9 ; another example is an elliptic fibration over a Hirzebruch surface. We compute the necessary amount of chiral matter by "turning on" a further parameter which is related to singularities of the fibration and the branching of the spectral cover.