Abstract
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 → eτV, where τ is an arbitrary real scalar superfield. We next propose a new Goldstino supermultiplet which is described by a nilpotent three-form superfield mathcal{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 mathcal{Y} may be obtained from a super-symmetric nonlinear σ-model in the infrared limit. Unlike V , the Goldstino superfield mathcal{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 mathcal{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.
Highlights
Where f is a positive parameter of mass dimension +2 which characterises the supersymmetry breaking scale
We demonstrate that every irreducible Goldstino superfield can be realised as a descendant of V which is invariant under local rescalings V → eτ V, where τ is an arbitrary real scalar superfield
We 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
Summary
We start by recalling two simple models for spontaneously broken supersymmetry that are realised in terms of an unconstrained real scalar superfield V. This is the only difference between the three-form multiplet and the standard scalar multipelt. The field strength (2.4) and the action (2.3) are invariant under gauge transformations δV = L , L = L , D 2L = 0 ,. In case V is subject to the nilpotency constraints (1.1), which are incompatible with the gauge symmetries (2.2) and (2.6), any difference between the actions (2.1) and (2.3) proves to disappear. Ψ Ψ D2Ψ + D 2Ψ (2.7b) which expresses the field strength of the gauge three-form, ImF , in terms of the Goldstino and ReF. The latter constraint follows from the observation that (1.3) may be rewritten in several equivalent forms.
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