Non-perturbative Effects in String Theory

We study non-perturbative effects generated by Euclidean brane instantons in compactifications of Type I/II string theory with orientifolds and magnetized D-branes. The focus is on instantons which can generate corrections to the superpotential. A necessary condition is that the instantons have to wrap rigid cycles. We consider the compactification of Type I (IIB) on the T^6/Z_2xZ_2 orientifold with discrete torsion and magnetized branes. The instantons wrapping the same cycle as the exotic O-planes (required by the presence of discrete torsion) have the desired uncharged zero-mode structure in order to generate corrections to the superpotential. We build global models based on this orientifold where stringy instantons generate linear terms and mass terms in the superpotential. Typically, in string theory one computes a physical coupling from which one has to extract a holomorphic part in order to obtain the non-perturbative superpotential. Various non-holomorphic factors are absorbed into the Kahler potential and redefinitions of chiral fields and closed string moduli. We have derived these redefinitions in the context of toroidal (orientifold) compactifications of Type I with magnetized branes and continuous Wilson lines. Finally, we have considered global models with linear terms in the superpotential generated non-perturbatively. We have computed explicitly the non-perturbative superpotential for toroidal orientifolds. We show how to sum coherently over the various one-instanton contributions. The explicit models analyzed possessed a non-perturbative supersymmetric vacuum where the gauge group was broken and certain open-string moduli were stabilized.