Higgs Mechanism and Luna Strata in N=1 Gauge Theories

TL;DR

This paper explores the stratification of the classical moduli space in N=1 supersymmetric gauge theories with non-zero superpotential, revealing new insights into gauge symmetry breaking, Higgs flows, and conditions for massless fields.

Contribution

It introduces an alternative method to analyze gauge symmetry breaking and construct superpotentials without knowing elementary matter content, aiding in supersymmetry breaking studies.

Findings

Patterns of gauge symmetry breaking differ from W=0 case.

Method for identifying heavy composite fields in effective superpotentials.

Conditions for null non singlet massless fields after Higgs mechanism.

Abstract

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 \neq 0 theory classical moduli space M^W \subset M, working entirely with the composite gauge invariant operators X that span M, assuming we do not known their elementary matter chiral field content. In this construction, the patterns of gauge symmetry breaking of the W \neq 0 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 X \in M^W among the moduli \delta X using the stratification of M, and establish conditions under which the space of non singlet massless fields after Higgs mechanism (unseen as moduli \delta X) 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.