Metastable spontaneous breaking of N=2 supersymmetry

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-Kähler and the special-Kähler 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.