Testing the FPS approach in d=1

Abstract

We apply the approach of S. Ferrara, M. Porrati and A. Sagnotti \cite{FPS} to the one dimensional system described by the $N=2, d=1$ supersymmetric action for two particles in which one of $N=1$ supersymmetries is spontaneously broken. Using the nonlinear realization approach we reconsider the system in the basis where only one superfield has the Goldstone nature while the second superfield can be treated as the matter one, being invariant under transformations of the spontaneously broken $N=1$ supersymmetry. We establish the transformations relating the two selected FPS-like cases with our more general one, and find the field redefinitions which relate these two cases. Thus we demonstrate, at least in one dimension, that the only difference between two FPS cases lies in the different choice of the actions, while the supermultiplets specified by the FPS-like constraints are really the same. Going further with the nonlinear realization approach, we construct the most general action for the system of two $N=1$ superfields possessing one additional hidden spontaneously broken $N=1$ supersymmetry. The constructed action contains two arbitrary functions and reduces to the FPS actions upon specification of these functions. Unfortunately, the exact form of these functions corresponding to FPS actions is not very informative and gives no explanation on why the FPS cases are selected.