A chiral D = 4, N = 1 string vacuum with a finite low energy effective field theory

Supersymmetric N = 1, D = 4 string vacua are known to be finite in perturbation theory. However, the effective low energy D = 4, N = 1 field theory lagrangian does not yield, in general, finite theories. In this note we present the first (to our knowledge) such example. It may be constructed in three dual ways: i) as a Z₃ , SO(32) heterotic orbifold; ii) as a type-IIB, Z₃ orientifold with only ninebranes and a Wilson line, or iii) as a type-IIB , Z₆ orientifold with only fivebranes. The gauge group is SU(4)³ with three chiral generations. Although chiral, a subsector of the model is continously connected to a model with global N = 4 supersymmetry. From the Z₆, type IIB orientifold point of view the above connection may be understood as a transition of four dynamical fivebranes from a fixed point to the bulk. The N = 1 model is, thus, also expected to be S-dual. We also remark that, using the untwisted dilaton and moduli fields of these constructions as spurion fields, soft SUSY-breaking terms which preserve finiteness even for N = 0 are yielded.