Superconformal vector multiplet self-couplings and generalised Fayet-Iliopoulos terms

As an extension of the recent construction of generalised Fayet-Iliopoulos terms in $\mathcal{N}=1$ supergravity given in [1], we present self-interactions for a vector multiplet coupled to conformal supergravity. They are used to construct new models for spontaneously broken local supersymmetry.