New duality-invariant models for nonlinear supersymmetric electrodynamics

We propose a new family of $\mathsf{U}(1)$ duality-invariant models for nonlinear ${\cal N}=1$ supersymmetric electrodynamics coupled to supergravity. It includes the Cribiori-Farakos-Tournoy-van Proeyen supergravity-matter theory for spontaneously broken local supersymmetry with a novel Fayet-Iliopoulos term without gauged $R$-symmetry. We present superconformal duality-invariant models, as well as new $\mathsf{U}(1)$ duality-invariant models for spontaneously broken local supersymmetry.