Light field integration in SUGRA theories

We study, in a supersymmetric manifest way, the possibility of having a reliable two-derivative N=1 Supergravity effective theory in situations where the fields that are mapped out have masses comparable to the supersymmetry breaking scale and the masses of the remaining fields. We find that in models with two chiral sectors, H and L, described by a Kaehler invariant function with schematic dependencies of the form G=G_H(H,\bar H)+G_L(L,\bar L) the superfield equation of motion \partial_H G=0 leads to a reliable two-derivative Supersymmetric description for the L sector upon requiring slowly varying solutions in the H one. The H fields can be charged only under a hidden gauge sector and the dependency of the visible gauge kinetic function on them should be suppressed, the same for the L-field dependency on the hidden gauge kinetic function. In this case the superfield vector equation \partial_V G=0 for the hidden sector is also necessary to get rid of the vector superfields, some of them now massive by gauge symmetry breaking, while mapping out unfixed chiral fields related to the would-be Goldstone directions. Our results coincide with the naive expectation of promoting to the superspace the F-flatness condition which despite the fact of not being a chiral superfield equation, for these kind of factorizable models, has solutions consistent with chiral superfields.