Three-form multiplet and supersymmetry breaking

Recently, a nilpotent real scalar superfield V was introduced in [1] as a model for the Goldstino. It contains only two independent component fields, the Goldstino and the auxiliary D-field. Here we first show that V can equivalently be realised as a constrained three-form superfield. We demonstrate that every irreducible Goldstino superfield (of which the Goldstino is the only independent component field) can be realised as a descendant of V which is invariant under local rescalings V → e^τV, where τ is an arbitrary real scalar superfield. We next propose a new Goldstino supermultiplet which is described by a nilpotent three-form superfield Y that is a variant formulation for the nilpotent chiral superfield, which is often used in off-shell models for spontaneously broken supergravity. It is shown that the action describing the dynamics of Y may be obtained from a super-symmetric nonlinear σ-model in the infrared limit. Unlike V , the Goldstino superfield Y contains two independent auxiliary fields, F = H + iG, of which H is a scalar and G is the field strength of a gauge three-form. When Y is coupled to supergravity, both H and G produce positive contributions to the cosmological constant. While the contribution from H is uniquely determined by the parameter of the supersymmetry breaking in the action, the contribution from G is dynamical.