Studying non-calculable models of dynamical supersymmetry breaking

There are supersymmetric gauge theories which do not possess any parameters nor flat directions, and hence they cannot be studied anywhere in the field space using holomorphy (“non-calculable”). Some of them are believed to break supersymmetry dynamically. We propose a simple technique to analyze these models. Introducing a vector-like field into the model, one finds flat directions where one can study the dynamics. We unambiguously show that the supersymmetry is broken when the mass of the vector-like field is small but finite, and hence the Witten index vanishes. If we increase the mass of the vector-like field, it eventually decouples from the dynamics and the models reduce to the original non-calculable models. Assuming continuity of the Witten index in the parameter space, one can establish dynamical supersymmetry breaking in the non-calculable models.