Singularities, gauge dynamics, and non-perturbative superpotentials in string theory

We describe a class of 4D N=1 compactifications of the SO(32) heterotic/type I string theory which are destabilized by non-perturbatively generated superpotentials. In the type I description, the destabilizing superpotential is generated by a one instanton effect or gaugino condensation in a non-perturbative SU(2) gauge group. The dual, heterotic description involves destabilization due to world-sheet instanton or half world-sheet instanton effects in the two cases. A genericity argument suggests that a (global) supersymmetry-breaking model of Intriligator and Thomas might be typical in a class of string theory models. Our analysis also suggests that the tensionless strings which arise in the E8 x E8 theory in six dimensions when an instanton shrinks to zero size should, in some cases, have supersymmetry breaking dynamics upon further compactification to four dimensions. We provide explicit examples, constructed using F-theory, of the two cases of dynamically generated superpotentials. (orig.)