We discuss how the higher-derivative Starobinsky model of inflation originates from N = 1 supergravity. It is known that, in the old-minimal supergravity description written by employing a chiral compensator in the superconformal framework, the Starobinsky model is equivalent to a no-scale model with F -term potential. We show that the Starobinsky model can also be originated within the so-called new-minimal supergravity, where a linear compensator superfield is employed. In this formulation, the Starobinsky model is equivalent to standard supergravity coupled to a massive vector multiplet whose lowest scalar component plays the role of the inflaton and the vacuum energy is provided by a D-term potential. We also point out that higher-order corrections to the supergravity Lagrangian represent a threat to the Starobinsky model as they can destroy the flatness of the inflaton potential in its scalar field equivalent description.

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 present a duality procedure that relates conventional four-dimensional matter-coupled N = 1 supergravities to dual formulations in which auxiliary fields are replaced by field strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the superpotential to vacuum expectation values of the field strengths. We then apply this general duality to type IIA string compactifications on Calabi-Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms.

We consider four-dimensional N = 1 supergravity models of a kind appearing in string flux compactifications. It has been recently shown that, by using double three-form multiplets instead of ordinary chiral multiplets, one can promote to dynamical variables (part of) the quantized numbers appearing in the flux-induced superpotential. We show that double three-form multiplets naturally transform under symplectic dualities associated with the special Kähler structure that characterizes their scalar sector. Furthermore, we discuss how to couple membranes which carry arbitrary 'electric-magnetic' charges. The complete action is supersymmetric, kappa-symmetric and duality covariant. As an application, we derive the flow equations for BPS domain walls sourced by membranes and give simple analytic examples of their solution.