Non-abelian discrete flavor symmetries from T2/Z N orbifolds

Abstract

In [1] it was shown how the flavor symmetry A 4 (or S 4) can arise if the three fermion generations are taken to live on the fixed points of a specific 2-dimensional orbifold. The flavor symmetry is a remnant of the 6-dimensional Poincaré symmetry, after it is broken down to the 4-dimensional Poincaré symmetry through compactification via orbifolding. This raises the question if there are further non-abelian discrete symmetries that can arise in a similar setup. To this end, we generalize the discussion by considering all possible 2-dimensional orbifolds and the flavor symmetries that arise from them. The symmetries we obtain from these orbifolds are, in addition to S 4 and A 4, the groups D 3, D 4 and D 6≃ D 3 × Z 2 which are all popular groups for flavored model building. © SISSA 2009.