Abstract
We build the minimal supergravity model where the nilpotent chiral goldstino superfield is coupled to a chiral matter superfield, realising a different non-linear representation through a mixed nilpotency constraint. The model describes the spontaneous breaking of local supersymmetry in the presence of a generically massive Majorana fermion, but in the absence of elementary scalars. The sign and the size of the cosmological constant, the spectrum and the four-fermion interactions are controlled by suitable parameters.
Highlights
There has been some progress in the embedding of non-linear realisations of N = 1, D = 4 supersymmetry in supergravity, spontaneously broken through the super-Higgs mechanism [1,2]
The most important feature of these models is the replacement of the elementary complex scalar of the goldstino multiplet, the sgoldstino [12], with a goldstino bilinear, and this makes them attractive to build simple semi-realistic models of inflation
The elementary complex scalars of the unconstrained matter chiral superfields still belong to the physical spectrum
Summary
Because of the nilpotency constraints, computing the spin-1/2 fermion masses requires a correction to the standard supergravity formula, and provide a simple formula for such a correction, which can be applied to non-minimal models with an arbitrary number of constrained chiral superfields. Both h and g/ f will affect the four-fermion interactions. S1 = X and S2 = Y , but the above formula can be generalised to an arbitrary number of constrained chiral multiplets, whose scalar components are replaced by fermion bilinears. Such a study would require the systematic derivation of the fermionic action and goes beyond the aim of the present letter
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