Abstract
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.
Highlights
It is well understood that the difficulty of achieving metastability for vacua leading to spontaneous supersymmetry breaking has a simple and universal origin related to Goldstone’s theorem applied to supersymmetry
The aim of this letter is to assess whether the possibility of having metastable supersymmetry breaking in N=2 theories is really linked to the presence of FayetIliopoulos terms
We have demonstrated that metastable spontaneous breaking of global N=2 supersymmetry is possible even in very simple theories that do not involve Fayet-Iliopoulos terms or non-Abelian gaugings
Summary
It is well understood that the difficulty of achieving metastability for vacua leading to spontaneous supersymmetry breaking has a simple and universal origin related to Goldstone’s theorem applied to supersymmetry. In theories with only hypermultiplets, supersymmetry breaking stationary points are possible only for curved geometries and the upper bound on the lightest mass happens to always vanish, as a consequence of the structure of the sectional curvature of hyper-Kahler manifolds This implies that there is always at least one tachyonic scalar, and that the vacuum cannot be metastable. The aim of this letter is to assess whether the possibility of having metastable supersymmetry breaking in N=2 theories is really linked to the presence of FayetIliopoulos terms For this we shall study in full generality the simplest class of such theories for which no-go theorems based on the sGoldstino masses do not exist so far, namely theories involving just one hypermultiplet and one vector multiplet with an Abelian gauge symmetry
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