A Note on Supersymmetry Breaking

TL;DR

This paper uses holomorphy to show that supersymmetry breaking or preservation in models is generally consistent across parameter ranges, with exceptions at isolated points, aiding in model construction.

Contribution

It introduces a simple holomorphy-based argument that constrains supersymmetry breaking behavior across parameter spaces, providing insights for model building.

Findings

Supersymmetry breaking occurs generically across parameters, except at isolated points.

Supersymmetry preservation also occurs generally, with exceptions at isolated points.

The results relate to the Witten index and aid in constructing supersymmetry-breaking models.

Abstract

Using a simple observation based on holomorphy, we argue that any model which spontaneously breaks supersymmetry for some range of a parameter will do so generically for all values of that parameter, modulo some isolated exceptional points. Conversely, a model which preserves supersymmetry for some range of a parameter will also do so everywhere except at isolated exceptional points. We discuss how these observations can be useful in the construction of new models which break supersymmetry and discuss some simple examples. We also comment on the relation of these results to the Witten index.