Metastable spontaneous breaking of N=2 supersymmetry

Understand

We show that contrary to the common lore it is possible to spontaneously break N=2 supersymmetry even in simple theories without constant Fayet-Iliopoulos terms.

• We consider the most general N=2 supersymmetric theory with one hypermultiplet and one vector multiplet without Fayet-Iliopoulos terms, and show that metastable supersymmetry breaking vacua can arise if both the hyper-Kahler and the special-Kahler geometries are suitably curved.
• We then also prove that while all the scalars can be massive, the lightest one is always lighter than the vector boson.
• Finally, we argue that these results also directly imply that metastable de Sitter vacua can exist in N=2 supergravity theories with Abelian gaugings and no Fayet-Iliopoulos terms, again contrary to common lore, at least if the cosmological constant is sufficiently large.