We present the component Lagrangian for the general coupling of N=1 matter to a higher curvature four-dimensional supergravity in which the (curvature)2 terms enter the Lagrangian only through the Gauss-Bonnet and Hirzebruch invariants. This is the situation suggested by the low-energy limit of heterotic strings, after compactification to four dimensions. The model obtained from the string by SU(3)-invariant truncation of the toroidal compactification is discussed in detail. We give the closed-form expression for the scalar potential and discuss supersymmetry breaking via gaugino condensation. We show that, in this last case, the cosmological constant Λ remains exactly zero even when the higher curvature corrections are taken into account. We also discuss briefly the problem of auxiliary field propagation and show that the spurious states decouple (i.e. they get an infinite mass) on the physical vacuum with Λ=0, irrespective of whether SUSY is broken or not. Some new, stringy, developments are discussed in the last section.
