SU(3) x SU(2) x U(1) Vacua in F-Theory

Understand

The Standard Model group and matter spectrum is obtained in vacua of F-theory, without resorting to an intermediate unification group.

• The group SU(3) x SU(2) x U(1)_Y is the commutant to SU(5)_t \times U(1)_Y structure group of a Higgs bundle in E_8 and is geometrically realized as a deformation of I_5 singularity.
• Lying along the unification groups of E_n, our vacua naturally inherit their unification structure.
• By modding SU(5)_t out by Z_4 monodromy group, we can distinguish Higgses from lepton doublets by matter parity.