  If the gravitino is light and all the other supersymmetric particles are
heavy, we can consider the effective theory describing the interactions of its
goldstino components with ordinary matter. To discuss the model-dependence of
these interactions, we take the simple case of spontaneously broken
supersymmetry and only two chiral superfields, associated with the goldstino
and a massless matter fermion. We derive the four-point effective coupling
involving two matter fermions and two goldstinos, by explicit integration of
the heavy spin-0 degrees of freedom in the low-energy limit. Surprisingly, our
result is not equivalent to the usual non-linear realization of supersymmetry,
where a pair of goldstinos couples to the energy-momentum tensor of the matter
fields. We solve the puzzle by enlarging the non-linear realization to include
a second independent invariant coupling, and we show that there are no other
independent couplings of this type up to this order in the low-energy
expansion. We conclude by commenting on the interpretation of our results and
on their possible phenomenological implications.
