A supersymmetric grand unified theory of flavour with PSL2(7)×SO(10)PSL2(7)×SO(10)

We construct a realistic Supersymmetric Grand Unified Theory of Flavour based on PSL2(7)×SO(10)PSL2(7)×SO(10), where the quarks and leptons in the 16 of SO(10)SO(10) are assigned to the complex triplet representation of PSL2(7)PSL2(7), while the flavons are assigned to a combination of sextets and anti-triplets of PSL2(7)PSL2(7). Using a D  -term vacuum alignment mechanism, we require the flavon sextets of PSL2(7)PSL2(7) to be aligned along the 3–3 direction leading to the third family Yukawa couplings, while the flavon anti-triplets describe the remaining Yukawa couplings. Other sextets are aligned along the neutrino flavour symmetry preserving directions leading to tri-bimaximal neutrino mixing via a type II see-saw mechanism, with predictions for neutrinoless double beta decay and cosmology.