Supersymmetry Breaking in Superstring Theory by Gaugino Condensation and its Phenomenology

The weakly-coupled heterotic string is known to have problems of dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), QCD axion, as well as cosmological problems. We study these problems by adopting the viewpoint that they arise mostly due to our limited calculational power, little knowledge of the vacuum structure, and an inappropriate treatment of gaugino condensation. It turns out that these problems can be solved or are much less severe after a more consistent and complete treatment. There are two kinds of non-perturbative effects in the construction of effective field theory: the field-theoretical non-perturbative effects of gaugino condensation (with a constraint ignored in the past) and the stringy non-perturbative effects conjectured by Shenker, which are best described using the linear multiplet formalism. Stringy non-perturbative corrections to the K\"ahler potential are invoked to stabilize the dilaton at a value compatible with a weak coupling regime. Modular invariance is ensured through the Green-Schwarz counterterm and string threshold corrections which, together with hidden matter condensation, lead to moduli stabilization at the self-dual point where the vev's of moduli's F-components vanish. In the vacuum, supersymmetry is broken at a realistic scale with vanishing cosmological constant. As for soft supersymmetry breaking, our model always leads to a dilaton-dominated scenario. For the strong CP problem, the model-independent axion has the right properties to be the QCD axion. Furthermore, there is a natural mass hierarchy between the dilaton/moduli and the gravitino, which could solve the cosmological moduli problem and the cosmological problem of the model-independent axion.