Multi-instanton and string loop corrections in toroidal orbifold models

We analyze N=2 (perturbative and non-perturbative) corrections to the effective theory in type I orbifold models where a dual heterotic description is available. These corrections may play an important role in phenomenological scenarios. More precisely, we consider two particular compactifications: the Bianchi-Sagnotti-Gimon-Polchinski orbifold and a freely-acting Z_2 x Z_2 orbifold with N=1 supersymmetry and gauge group SO(q) x SO(32-q). By exploiting perturbative calculations of the physical gauge couplings on the heterotic side, we obtain multi-instanton and one-loop string corrections to the K\"ahler potential and the gauge kinetic function for these models. The non-perturbative corrections appear as sums over relevant Hecke operators, whereas the one-loop correction to the K\"ahler potential matches the expression proposed in [1,2]. We argue that these corrections are universal in a given class of models where target-space modular invariance (or a subgroup of it) holds.