Unified model of fermion masses with Wilson-line flavor symmetry breaking

Abstract

We present a supersymmetric $SU(5)$ grand unified theory model with a discrete non-Abelian flavor symmetry that is broken by Wilson lines. The model is formulated in $4+3$ dimensions compactified on a manifold ${S}^{3}/{Z}_{n}$. Symmetry breaking by Wilson lines is topological and allows to realize the necessary flavor symmetry breaking without a vacuum alignment mechanism. The model predicts the hierarchical pattern of charged fermion masses and quark mixing angles. Small normal hierarchical neutrino masses are generated by the type-I seesaw mechanism. The non-Abelian flavor symmetry predicts to leading order exact maximal atmospheric mixing while the solar angle emerges from a variant of quark-lepton complementarity. As a consequence, the resulting leptonic mixing matrix is in excellent agreement with current data and could be tested in future neutrino oscillation experiments.