Building SO10_{10}- models with D4\mathbb{D}_{4} symmetry

Using characters of finite group representations and monodromy of matter curves in F-GUT, we complete partial results in literature by building SO$_{10}$ models with dihedral $\mathbb{D}_{4}$ discrete symmetry. We first revisit the $\mathbb{S}_{4}$-and $\mathbb{S}_{3}$-models from the discrete group character view, then we extend the construction to $\mathbb{D}_{4}$.\ We find that there are three types of $SO_{10}\times \mathbb{D}_{4}$ models depending on the ways the $\mathbb{S}_{4}$-triplets break down in terms of irreducible $\mathbb{D}_{4}$- representations: $\left({\alpha} \right)$ as $\boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{-,+}};$ or $\left({\beta}\right) \boldsymbol{\ 1}_{_{+,+}}\oplus \boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{-,-}};$or also$\left({\gamma}\right) $$\mathbf{1}_{_{+,-}}\oplus \mathbf{2}_{_{0,0}}$. Superpotentials and other features are also given.Comment: 20 pages, Nuclear Physics B (2015

MSSM-like from SU5×D4SU_{5}\times D_{4} Models

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.Comment: 48 pages, LaTe

Fermion masses and mixing in SU(5)×D4×U(1) model

We propose a supersymmetric SU(5)×Gf GUT model with flavor symmetry Gf=D4×U(1) providing a good description of fermion masses and mixing. The model has twenty eight free parameters, eighteen are fixed to produce approximative experimental values of the physical parameters in the quark and charged lepton sectors. In the neutrino sector, the TBM matrix is generated at leading order through type I seesaw mechanism, and the deviation from TBM studied to reconcile with the phenomenological values of the mixing angles. Other features in the charged sector such as Georgi–Jarlskog relations and CKM mixing matrix are also studied