An $S_4 \times SU(5)$ SUSY GUT of flavour in 6d

Abstract

We propose a 6d model with a SUSY $SU(5)$ gauge symmetry. After compactification, it explains the origin of the $S_4$ Family Symmetry with CSD3 vacuum alignment, as well as $SU(5)$ breaking with doublet-triplet splitting. The model naturally accounts for all quark and lepton (including neutrino) masses and mixings, incorporating the highly predictive Littlest Seesaw structure. It spontaneously breaks CP symmetry, resulting in successful CP violation in the quark and lepton sectors, while solving the Strong CP problem. It also explains the Baryon Asymmetry of the Universe (BAU) through leptogenesis, with the leptogenesis phase directly linked to the Dirac and Majorana phases.