Z3 flavor symmetry and possible implications

We show in this Letter that the Z3 flavor symmetry, which can successfully produces the tri-bimaximal mixing and flavor pattern of neutrino sector, has a possible explanation in the framework of gauge symmetry by constructing a wavefunction of flavor state particles with the help of the Wilson loop. In this implementation of Z3 flavor symmetry, we suggest that the flavor charge in weak interaction can be interpreted as topological charge. Its possible implications and generalizations to the quark sector are also discussed.