Exact Results And Soft Breaking Masses In Supersymmetric Gauge Theory

TL;DR

This paper develops a formalism linking softly broken supersymmetric gauge theories to exact solutions in higher supersymmetry models, revealing how soft breaking affects vacuum structure and confinement phenomena.

Contribution

It introduces a method to connect softly broken supersymmetric theories with exact solutions in N=1 and N=2 models using spurion fields, and analyzes the impact on monopole condensation.

Findings

Soft breaking masses perturb exact N=1 results.

Existence of nonsupersymmetric models with monopole condensation.

Confinement mechanisms similar to supersymmetric cases.

Abstract

We give an explicit formalism connecting softly broken supersymmetric gauge theories (with QCD as one limit) to $N=2$ and $N=1$ supersymmetric theories possessing exact solutions, using spurion fields to embed these models in an enlarged $N=1$ model. The functional forms of effective Lagrangian terms resulting from soft supersymmetry breaking are constrained by the symmetries of the enlarged model, although not well enough to fully determine the vacuum structure of generic softly broken models. Nevertheless by perturbing the exact $N=1$ model results with sufficiently small soft breaking masses, we show that there exist nonsupersymmetric models that exhibit monopole condensation and confinement in the same modes as the $N=1$ case.