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

TL;DR

This paper constructs F-theory vacua with the Standard Model gauge group directly, deriving matter content and Yukawa couplings without intermediate unification groups, highlighting geometric and flux-based mechanisms.

Contribution

It presents a geometric realization of the Standard Model gauge group in F-theory as a deformation of singularities, with matter parity and realistic spectrum achieved through fluxes.

Findings

Realization of SM gauge group as a deformation of I_5 singularity

Spectrum includes three generations of quarks and leptons

Minimal Yukawa couplings are obtained at the renormalizable level

Abstract

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. 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.