• strong coupling
• String Theory
• integrable models
• compactification
• brane supersymmetry breaking
• supersymmetry

In this thesis we want to deal with the issue of supersymmetry breaking in string theory, a fundamental problem that has been elusive for many years. In particular, we focus on three non-tachyonic non-supersymmetric theories: the USp(32) model with Brane Supersymmetry Breaking, the U(32) 0′B model and the heterotic SO(16)×SO(16) model, in which supersymmetry is broken at the string scale or not present at all. The classical vacua found in a work by E. Dudas and J. Mourad, central for this thesis, present several peculiar features, such as a dynamically compactified dimension and regions where the solution is not reliable, lying beyond regimes where perturbative String Theory applies. This emergence of a modified dynamics is a recurring trait of non-supersymmetric models, which renders them extremely complicated to analyze. The aim of this work is to shed light in this direction, in particular to understand if perturbative and non-perturbative contributions in the low energy effective theory can cure the non-reliable regions of the Dudas and Mourad solutions. We proceed in this program analyzing different models that closely resemble the low energy effective actions arising from string theories, taken from a paper by P. Fré, A. Sagnotti and A.S. Sorin. Although we expect that the potentials considered do not have a precise String Theory counterpart, we choose them integrable, to overcome the technical difficulties of the system of coupled equations of motion. Integrability let us gain complete control over the solutions found, thus being an invaluable tool for our analysis.
In the original part of this work we argue that one equation of motion, which is usually called the Hamiltonian constraint, can be successfully used to rule out potentials that produce strong coupling regions; in all other ones, we find several examples with very different potentials that display well behaved solutions, in which the string coupling constant is always perturbative and one dimension is dynamically compactified. For these reasons we argue that there are at least two ways in which String Theory can cure the non-reliable regions of the Dudas and Mourad solutions. One is through non-perturbative contributions, which may help in maintaining the string coupling constant perturbative by confining the dilaton within an upper bound. The other is to consider dilaton potentials defined only for negative values of the dilaton, forcing the string coupling constant to be perturbative by construction; in this case, a dynamically compactified direction is not guaranteed, but we have considered an example of this sort which displays this feature.