MSSM-like from SU5×D4 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 SU5×D4 models embedded in F-theory with non-abelian flux. Matter curves spectrum of the models is obtained from SU5×S5 theory with monodromy S5 by performing two breakings: first from symmetric group S5 to S4 subsymmetry, and next to dihedral D4 subgroup. As a consequence, and depending on the ways of decomposing triplets of S4, we end with three types of D4-models. Explicit constructions of these theories are given and a MSSM-like spectrum is derived.