Systematic classification of aGUT models in five dimensions: The SU(N) kinship

Asymptotic Grand Unification theories (aGUTs) in five dimensions provide a valid alternative to standard quantitative unification. We define the pathway towards viable models starting from a general unified bulk gauge symmetry. Imposing the presence of ultra-violet fixed points for both gauge and Yukawa couplings strongly limits the possibilities. Within the SU(N) kinship, we identify and characterise only two realistic minimal models, both based on a bulk SU(6) symmetry. Both models feature the generation of either up or down-type Yukawas via gauge scalars, two Higgs doublets with build-in minimal flavour violation at low energies, and conservation of baryon number. We also propose interesting avenues beyond the minimality criterion.