Supersymmetric models with product groups and field dependent gauge couplings

We study the dilaton-dependence of the effective action for N=1, SU(N1) xSU(N2) models with one generation of vectorlike matter transforming in thefundamental of both groups. We treat in detail the confining and Coulomb phasesof these models writing explicit expressions in many cases for the effectivesuperpotential. We can do so for the Wilson superpotentials of the Coulombphase when N2=2, N1=2,4. In these cases the Coulomb phase involves a single U(1) gauge multiplet, forwhich we exhibit the gauge coupling in terms of the modulus of an ellipticcurve. The SU(4) x SU(2) model reproduces the weak-coupling limits in anontrivial way. In the confining phase of all of these models, the dilatonsuperpotential has a runaway form, but in the Coulomb phase the dilaton enjoysflat directions. Had we used the standard moduli-space variables: Tr M^k,k=1,..., N2, with M the quark condensate matrix, to parameterize the flatdirections instead of the eigenvalues of M, we would find physicallyunacceptable behaviour, illustrating the importance to correctly identify themoduli.Comment: 39 pages, plain TeX, no figures. (This paper replaces our earlier, withdrawn, paper, hep-th/9712178.) Minor typos correcte