Abstract :
The Standard Model group and matter spectrum is obtained in vacua of F-theory, without resorting to an intermediate unification group. The group image is the commutant to image structure group of a Higgs bundle in image and is geometrically realized as a deformation of image singularity. Lying along the unification groups of image, our vacua naturally inherit their unification structure. By modding image out by image monodromy group, we can distinguish Higgses from lepton doublets by matter parity. Turning on universal G-flux on this part, the spectrum contains three generations of quarks and leptons, as well as vectorlike pairs of electroweak and colored Higgses. Minimal Yukawa couplings is obtained at the renormalizable level.
