Supersymmetry Breaking and Determination of the Unification Gauge Coupling Constant in String Theories

Abstract

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 ($\mathrm{Re}S\sim g_{gut}^{-2}$). For the case of pure Yang--Mills condensation, we show that no realistic results (in particular no reasonable values for $\mathrm{Re}S$) 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 ($\mathrm{Re}S\sim 2$) and supersymmetry is broken at the correct scale ($m_{3/2}\sim 10^{3}GeV$) with no need of fine--tuning. Actually, good values for $\mathrm{Re}S$ and $m_{3/2}$ are correlated. We make an exhaustive classification of the working possibilities. Remarkably, the results are basically independent from the value of ${\delta }^{GS}$ (the contributions from the Green--Schwarz mechanism). The radius of the compactified space also acquires an expectation value, breaking duality spontaneously.

35 pages

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