We discuss, using the Hilbert basis method, how to efficiently construct a complete basis for D-flat directions in supersymmetric Abelian and non-Abelian gauge theories. We extend the method to discrete (R and non-R) symmetries. This facilitates the construction of a basis of all superpotential terms in a theory with given symmetries.

We discuss the predictive power of supersymmetric models with flavor symmetries, focusing on the lepton sector of the standard model. In particular, we comment on schemes in which, after certain 'flavons' acquire their vacuum expectation values (VEVs), the charged lepton Yukawa couplings and the neutrino mass matrix appear to have certain residual symmetries. In most analyses, only corrections to the holomorphic superpotential from higher-dimensional operators are considered (for instance, in order to generate a realistic θ 13 mixing angle). In general, however, the flavon VEVs also modify the Kähler potential and, therefore, the model predictions. We show that these corrections to the naive results can be sizable. Furthermore, we present simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. © 2012.

The well-known Giudice-Masiero mechanism explains the presence of a μ term of the order of the gravitino mass, but does not explain why the holomorphic mass term is absent in the supzerpotential. We discuss anomaly-free discrete symmetries which are both compatible with SU(5) unification of matter and the Giudice-Masiero mechanism, i.e. forbid the μ term in the superpotential while allowing the necessary Kähler potential term. We find that these are ZMR symmetries with the following properties: (i) M is a multiple of four; (ii) the Higgs bilinear H uH d transforms trivially; (iii) the superspace coordinate θ has charge M/4 and, accordingly, the superpotential has charge M/2; (iv) dimension-five proton decay operators are automatically absent. All ZMR symmetries are anomaly-free due to a non-trivial transformation of a Green-Schwarz axion, and, as a consequence, a holomorphic μ term appears at the non-perturbative level. There is a unique symmetry that is consistent with the Weinberg operator while there is a class of ZMR symmetries which explain suppressed Dirac neutrino masses. © 2012 Elsevier B.V.

In a class of supersymmetric flavor models predictions are based on residual symmetries of some subsectors of the theory such as those of the charged leptons and neutrinos. However, the vacuum expectation values of the so-called flavon fields generally modify the Kähler potential of the setting, thus changing the predictions. We derive simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. Furthermore, we discuss the effects on the vacuum alignment and on flavor changing neutral currents. Our results can also be applied to non-supersymmetric flavor models. © 2013 Elsevier B.V.