2013/09/30 by Kang-Sin Choi · 2 citations
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Combinatorics #Fermion #Gauge (firearms) #Gauge group #Gauge theory #Group (periodic table) #Hypercharge #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Rank (graph theory) #Section (typography) #Standard Model (mathematical formulation) #Theoretical physics #hep-th
paper · pdf · doi:10.1140/epjc/s10052-014-2939-7
29 pages
arxiv created 2013/11/15 · openalex publication_date 2014/06/01 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the standard model gauge group SU(3)× SU(2) × U(1) constructed in F-theory. The non-Abelian part SU(3) × SU(2) is described by a surface singularity of Kodaira type. Blow-up analysis shows that the non-Abelian part is distinguished from the naïve product of SU(3) and SU(2) , but that it should be a rank three group along the chain of En groups, because it has non-generic gauge symmetry enhancement structure responsible for desirable matter curves. The Abelian part U(1) is constructed from a globally valid two-form with the desired gauge quantum numbers, using a similar method to the decomposition (factorization) method of the spectral cover. This technique makes use of an extra section in the elliptic fiber of the Calabi–Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU(5) is achieved, without requiring a threshold correction from the flux along the hypercharge direction.