Higgs mechanism and Luna strata in N=1 gauge theories

The classical moduli space M of a supersymmetric gauge theory with trivial superpotential can be stratified according to the unbroken gauge subgroup at different vacua. We apply known results about this stratification to obtain the W≠0 theory classical moduli space MW is a subset of M, working entirely with the composite gauge invariant operators phi-circumflex that span M, assuming we do not know their elementary matter chiral field content. In this construction, the patterns of gauge symmetry breaking of the W≠0 zero theory are determined, Higgs flows in these theories show important differences from the W=0 case. The methods here introduced provide an alternative way to construct tree level superpotentials that lift all classical flat directions leaving a candidate theory for dynamical supersymmetry breaking, and are also useful to identify heavy composite fields to integrate out from effective superpotentials when the elementary field content of the composites is unknown. We also show how to recognize the massless singlets after Higgs mechanism at a vacuum phi-circumflex is a subset of NW among the moduli δphi-circumflex using the stratification of M, and establish conditions under which the space of non singlet massless fields after Higgs mechanism (unseen as moduli δphi-circumflex) is null. A small set of theories with so called 'unstable' representations of the complexified gauge group is shown to exhibit unexpected properties regarding the dimension of their moduli space, and the presence of non singlet massless fields after Higgs mechanism at all of their vacua