Studying Non-calculable Models of Dynamical Supersymmetry Breaking

TL;DR

This paper introduces a new technique to analyze non-calculable supersymmetric gauge theories, demonstrating dynamical supersymmetry breaking by adding a vector-like field and studying the resulting flat directions.

Contribution

A simple method using a vector-like field to analyze non-calculable models and prove supersymmetry breaking, extending understanding of these complex theories.

Findings

Supersymmetry is broken when the vector-like field's mass is small but finite.

The Witten index vanishes in these models, indicating supersymmetry breaking.

Continuity of the Witten index suggests supersymmetry breaking in original models.

Abstract

There are supersymmetric gauge theories which do not possess any parameters nor flat directions, and hence 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 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 the continuity of the Witten index in the parameter space, one can establish the dynamical supersymmetry breaking in the non-calculable models.