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 an example. It may be constructed in three dual ways: i) as a $Z_3$, SO(32) heterotic orbifold; ii) as a Type -IIB, $Z_3$ orientifold with only ninebranes and a Wilson line or iii) as a Type-IIB, $Z_6$ orientifold with only fivebranes. The gauge group is $SU(4)^3$ with three chiral generations. Although chiral, a subsector of the model is continuosly connected to a model with global N=4 supersymmetry. From the $Z_6$, 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, yields soft SUSY-breaking terms which preserve finiteness even for N=0. 
Luis E. Ibanez