Two-form supergravity, superstring couplings, and Goldstino superfields in three dimensions

We develop off-shell formulations for $\mathcal{N}=1$ and $\mathcal{N}=2$ anti-de Sitter supergravity theories in three spacetime dimensions that contain gauge two-forms in the auxiliary field sector. These formulations are shown to allow consistent couplings of supergravity to the Green-Schwarz superstring with $\mathcal{N}=1$ or $\mathcal{N}=2$ spacetime supersymmetry. In addition to being $\kappa$-symmetric, the Green-Schwarz superstring actions constructed are also invariant under super-Weyl transformations of the target space. We also present a detailed study of models for spontaneously broken local supersymmetry in three dimensions obtained by coupling the known off-shell $\mathcal{N}=1$ and $\mathcal{N}=2$ supergravity theories to nilpotent Goldstino superfields.