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

We develop off-shell formulations for N=1 and 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 N=1 or N=2 spacetime supersymmetry. In addition to being κ-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 N=1 and N=2 supergravity theories to nilpotent Goldstino superfields.