One of the original reasons for interest in supersymmetry was the possibility of dynamical supersymmetry breaking. So far, however, we have exhibited models in which supersymmetry is unbroken, as in the case of QCD with only massive quarks, or models with moduli spaces or approximate moduli spaces. In this section, we describe a number of models in which non-trivial dynamics breaks supersymmetry. We will see that the dynamical supersymmetry breaking occurs under special, but readily understood, conditions. In some cases, we will be able to exhibit this breaking explicitly, through systematic calculations. In others, we will have to invoke more general arguments.

Models of dynamical supersymmetry breaking

We might ask why, so far, we have not found supersymmetry to be dynamically broken. In supersymmetric QCD with massive quarks, we might give the index as an explanation. We might also note that there is not a promising candidate for a goldstino. With massless quarks, we have flat directions, and as the fields get larger, the theory becomes more weakly coupled, so any potential tends to zero. This suggests two criteria for finding models with dynamical supersymmetry breaking.

1. (1) The theory should have no flat directions at the classical level.

2. (2) The theory should have a spontaneously broken global symmetry.

The second criterion implies the existence of a Goldstone boson. If supersymmetry is unbroken, any would-be Goldstone boson must lie in a multiplet with another scalar, as well as aWeyl fermion. This other scalar, like the Goldstone particle, has no potential, so the theory has a flat direction. But by assumption, the theory classically (and therefore almost certainly quantum mechanically) has no flat direction.