On the Standard Model Group in F-theory

Understand

We analyze the Standard Model gauge group SU(3) x SU(2) x U(1) constructed in F-theory.

• The non-Abelian part SU(3) x SU(2) is described by singularities of Kodaira type.
• It is distinguished to naive product of SU(3) and SU(2), revealed by blow-up analysis, since the resolution procedures cannot be done separately to each group.
• The Abelian part U(1) is constructed by obtaining a desirable global two-form harboring it, using `factorization method' similar to the decomposition method of the spectral cover; It makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified.