2023/04/12 by Dmitry Manning-Coe, Manning-Coe, Dmitry
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2304.05394
openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this dissertation we attempt to answer the question of whether non-abelian gauge groups occur in all F-theory models with Picard number 20 and with a Calabi-Yau four-fold CY4 K3xK3. To do so we employ the Kneser-Nishiyama method to study the properties of elliptic fibrations on a K3 surface. Previously, it was found that there are 34 lattices which must be considered and the question was partially answered for one of them. Here we use results in the sphere packing problem to completely answer this question for 21 cases, and show that a negative answer to this question would constitute a new optimal lattice sphere packing in dimension 18.