Supersymmetry breaking and determination of the unification gauge coupling constant in string theories

We study in a systematic and modular invariant way gaugino condensation in the hidden sector as a potential source of hierarchical supersymmetry breaking and a non-trivial potential for the dilaton S whose real part corresponds to the tree-level gauge coupling constant (Re S ∼ ggut−2). For the case of pure Yang-Mills condensation, we show that no realistic results (in particular no reasonable values for Re S) can emerge, even if the hidden gauge group is not simple. However, in the presence of hidden matter (i.e. the most frequent case) there arises a very interesting class of scenarios with two or more hidden condensing groups for which the dilaton dynamically acquires a reasonable value (Re S ∼ 2) and supersymmetry is broken at the correct scale (m32∼103 GeV with no need of fine-tuning. Actually, good values for Re S and m32 are correlated. We make an exhaustive classification of the working possibilities. Remarkably, the results are basically independent from the value of δGS (the contributions from the Green-Schwarz mechanism). The radius of the compactified space also acquires an expectation value, breaking duality spontaneously.