We construct a supergravity-Maxwell theory with a novel embedding of the Fayet-Iliopoulos D-term, leading to spontaneous supersymmetry breaking. The gauging of the R-symmetry is not required and a gravitino mass is allowed for a generic vacuum. When matter couplings are introduced, an uplift through a positive definite contribution to the scalar potential is obtained. We observe a notable similarity to the D3 uplift constructions and we give a natural description in terms of constrained multiplets.

We consider the swampland distance and de Sitter conjectures, of respective order one parameters λ and c. Inspired by the recent Trans-Planckian Censorship conjecture (TCC), we propose a generalization of the distance conjecture, which bounds λ to be a half of the TCC bound for c, i.e. $$ \lambda \ge \frac{1}{2}\sqrt{\frac{2}{3}} $$ λ ≥ 1 2 2 3 in 4d. In addition, we propose a correspondence between the two conjectures, relating the tower mass m on the one side to the scalar 1 potential V on the other side schematically as $$ m\sim {\left|V\right|}^{\frac{1}{2}} $$ m ∼ V 1 2 , in the large distance limit. These proposals suggest a generalization of the scalar weak gravity conjecture, and are supported by a variety of examples. The lower bound on λ is verified explicitly in many cases in the literature. The TCC bound on c is checked as well on ten different no-go theorems, which are worked-out in detail, and V is analysed in the asymptotic limit. In particular, new results on 4d scalar potentials from type II compactifications are obtained.

We study field theories with N extended non-linearly realized supersymmetries, describing the couplings of models that contain N goldstini. We review all the known formulations of the N = 1 goldstino theories and we generalize them to an arbitrary number N of non-linearly realized supersymmetries. We explicitly prove the equivalence of all these extended supersymmetry breaking models containing N goldstini and reformulate the theory with N supersymmetries in terms of standard N = 1 constrained superfields.