Non Supersymmetric Vacua and the D-flatness Condition

TL;DR

This paper explores the structure of vacua in certain gauge theories, showing that non-supersymmetric vacua can be characterized similarly to supersymmetric ones using gauge invariants, with implications for understanding moduli spaces.

Contribution

It extends the parametrization of vacua via holomorphic invariants from supersymmetric to non-supersymmetric cases in gauge theories.

Findings

Stationary points of V are D-flat in some theories.

Non-supersymmetric vacua can be described using gauge invariants.

Method applies to non-gauge theories with global symmetries.

Abstract

Some N=1 gauge theories, including SQED and N_F=1 SQCD have the property that, for arbitrary superpotentials, all stationary points of the potential V = F+D are D-flat. For others, stationary points of V are complex gauge transformationss of D-flat configurations. As an implication, the technique to parametrize the moduli space of supersymmetric vacua in terms of a set of basic holomorphic G invariants can be extended to non-supersymmetric vacua. A similar situation is found in non-gauge theories with a compact global symmetry group.