Continuous degeneracy of non-supersymmetric vacua

Understand

In global supersymmetric Wess-Zumino models with minimal K\"ahler potentials, F-type supersymmetry breaking always yields instability or continuous degeneracy of non-supersymmetric vacua.

• As a generalization of the original O'Raifeartaigh's result, the existence of instability or degeneracy is true to any higher order corrections at tree level for models even with non-renormalizable superpotentials.
• The degeneracy generically coincides the R-axion direction under some assumptions of R-charge assignment, but generally requires neither R-symmetries nor any assumption of generic superpotentials.
• The result also confirms the well-known fact that tree level supersymmetry breaking is a very rare occurrence in global supersymmetric theories with minimal K\"ahler potentials.