S4 as a natural flavor symmetry for lepton mixing

Group theoretical arguments seem to indicate the discrete symmetry S4 as the minimal flavor symmetry compatible with tribimaximal neutrino mixing. We prove in a model-independent way that indeed S4 can realize exact tribimaximal mixing through different symmetry breaking patterns. We present two models in which lepton tribimaximal mixing is realized in different ways and for each one we discuss the superpotential that leads to the correct breaking of the flavor symmetry.