A Geometry of the Generations

Abstract

We propose a geometric theory of flavor based on the discrete group $(S_3)^3$, in the context of the minimal supersymmetric standard model. The group treats three objects symmetrically, while making fundamental distinctions between the generations. The top quark is the only heavy quark in the symmetry limit, and the first and second generation squarks are degenerate. The hierarchical nature of Yukawa matrices is a consequence of a sequential breaking of $(S_3)^3$.