Stringy instantons and Yukawa couplings in MSSM-like orientifold models

Type IIA orientifold constructions with intersecting D6-branes and their IIB duals in terms of magnetized D9/D7-branes constitute one of the most promising avenues for the construction of semirealistic MSSM-like compactifications. One generic problem with these constructions is that there are many Yukawa couplings, which vanish due to additional U(1) symmetries in the theory. In this paper, we consider a number of such settings and study under what conditions stringy instanton effects can give rise to non-perturbative contributions to the Yukawa couplings, so that all perturbatively forbidden terms are induced. We find specific settings in which Yukawa couplings for all fermions are indeed obtained. For some cases we provide specific local examples of rigid O(1) instantons within the T-6/Z(2) x Z(2)' toroidal orientifold with torsion that gives rise to the required amplitudes. A potential problem in these settings is that the same instantons, providing for Yukawa coupling contributions, may give rise to too large mu-terms for the Higgs multiplets. We show how this problem may be overcome in explicit models with a doubled Higgs system.