MSSM-like from $SU_{5}\times D_{4}$ Models

TL;DR

This paper constructs MSSM-like models within F-theory based on an SU(5) gauge group combined with a D4 discrete symmetry, utilizing symmetry breaking and matter curve analysis to derive realistic particle spectra.

Contribution

It introduces a novel method of deriving MSSM-like models from SU(5)×D4 in F-theory by symmetry breaking from S5 to D4, providing explicit constructions and spectra.

Findings

Derived three types of D4 models with MSSM-like spectra

Implemented symmetry breaking from S5 to D4 to obtain matter curves

Explicitly constructed models demonstrating realistic particle content

Abstract

Using finite discrete group characters and symmetry breaking by hyperflux as well as constraints on top- quark family, we study minimal low energy effective theory following from SU$_{5}\times D_{4}$ models embedded in F-theory with non abelian flux. Matter curves spectrum of the models is obtained from SU$_{5}\times S_{5}$ theory with monodromy $S_{5}$ by performing two breakings; first from symmetric group $S_{5}$ to $S_{4}$ subsymmetry; and next to dihedral $D_{4}$ subgroup. As a consequence, and depending on the ways of decomposing triplets of $S_{4}$, we end with three types of $D_{4}$- models. Explicit constructions of these theories are given and a MSSM- like spectrum is derived.