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 a t different vacua. We apply known results about this stratification to obta in the W not equal 0 theory classical moduli space M-W subset of M, working entirely with the composite gauge invariant operators <(<phi>)over cap> th at span M, assuming we do not know their elementary matter chiral field con tent. In this construction, the patterns of gauge symmetry breaking of the W not equal 0 zero theory are determined, Higgs flows in these theories sho w important differences from the W = 0 case. The methods here introduced pr ovide an alternative way to construct tree level superpotentials that lift all classical Bat directions leaving a candidate theory for dynamical super symmetry breaking, and are also useful to identify heavy composite fields t o integrate out from effective superpotentials when the elementary field co ntent of the composites is unknown. We also show how to recognize the massl ess singlets after Higgs mechanism at a vacuum <(<phi>)over cap> is an elem ent of M-W among the moduli delta<(<phi>)over cap> using the stratification of M, and establish conditions under which the space of non singlet massle ss fields after Higgs mechanism (unseen as moduli delta<(<phi>)over cap>) i s null. A small set of theories with so called "unstable" representations o f the complexified gauge group is shown to exhibit unexpected properties re garding the dimension of their moduli space, and the presence of non single t massless fields after Higgs mechanism at all of their vacua. (C) 2000 Els evier Science B.V. All rights reserved.