ar X iv : h ep - p h / 92 10 21 9 v 1 7 O ct 1 99 2 Gaugino condensation in 4 - D superstring models

We study the possibility that supersymmetry is broken via a gaugino condensate in four dimensional string theories. We derive an effective low-energy theory describing the Goldstone mode associated with the Rsymmetry breaking driven by gaugino condensation and show that this gives a description of gaugino condensation equivalent, at tree level, to other effective Lagrangian approaches based on the symmetries of the theory. A study of the mass gap equation shows that non-perturbative effects favour the appearance of a gaugino condensate. By minimizing the effective potential describing both the condensate and the moduli determining the gauge coupling constant and radius of compactification we show that large hierarchy may occur between the gravitino mass and the Planck mass with the existence of only one gaugino condensate. Associated with this is a determination of the fine structure constant and the compactification scale.