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.
We propose an extension of tri-bimaximal mixing to include a non-zero reactor angle $theta_{13}$ while maintaining the tri-bimaximal predictions for the atmospheric angle $theta_{23}=45^o$ and solar angle $theta_{12}=35^o$. We show how such tri-bimax
imal-reactor mixing can arise at leading order from the(type I) see-saw mechanism with partially constrained sequential dominance. Partially constrained sequential dominance can be realized in GUT models with a non-Abelian discrete family symmetry, such as $A_4$, spontaneously broken by flavons with a particular vacuum alignment.
We show how the SUSY flavour and CP problems can be solved using gauged SU(3) family symmetry previously introduced to describe quark and lepton masses and mixings, in particular neutrino tri-bimaximal mixing via constrained sequential dominance. The
Yukawa and soft trilinear and scalar mass squared matrices and kinetic terms are expanded in powers of the flavons used to spontaneously break the SU(3) family symmetry, and the canonically normaliz
