Hexagonal theory of flavor

We construct a supersymmetric theory of flavor based on the discrete gauge group ${(D}_6{)}^2,$ where $D_6$ describes the symmetry of a regular hexagon under proper rotations in three dimensions. The representation structure of the group allows one to distinguish the third from the lighter two generations of matter fields, so that in the symmetry limit only the top quark Yukawa coupling is allowed and scalar superpartners of the first two generations are degenerate. Light fermion Yukawa couplings arise from a sequential breaking of the flavor symmetry, and supersymmetric flavor-changing processes remain adequately suppressed. We contrast our model with others based on non-Abelian discrete gauge symmetries described in the literature and discuss the challenges in constructing more minimal flavor models based on this approach.