We propose an SU(5) SUSY GUT of flavour with A_4 family symmetry in 8d where the vacuum alignment is achieved in an elegant way by the use of boundary conditions on orbifolds. The model involves SU(5) living in the 8d bulk, with matter living in 6d (
or 4d) subspaces and Yukawa interactions occurring at a 4d point. The GUT group is broken to the Standard Model by the orbifold compactification, setting the GUT scale and leading to low energy supersymmetry and Higgs doublet-triplet splitting. The first two families of 10-plets are doubled resulting in a lack of both desirable and unwanted GUT relations. The resulting four dimensional effective superpotential leads to a realistic description of quark and lepton masses and mixing angles including tri-bimaximal neutrino mixing and an inter-family mass hierarchy provided in part by volume suppression and in part by a Froggatt-Nielsen mechanism.
We propose a model in which $A_4$ Family Symmetry arises dynamically from a six dimensional orbifold SU(5) Supersymmetric Grand Unified Theory. The SU(5) is broken to the Standard Model gauge group by a particular orbifold compactification leading to
$A_4$ Family Symmetry, low energy Supersymmetry and Higgs doublet-triplet splitting. The resulting four dimensional effective superpotential leads to a realistic description of quark and lepton masses and mixing angles including tri-bimaximal neutrino mixing and an inter-family mass hierarchy provided by a Froggatt-Nielsen mechanism. This model is the first which combines the idea of orbifold GUTs with $A_4$ family symmetry resulting from the orbifolding.
