multi-instanton and string-loop corrections in toroidal orbifold models

The low energy limit of String Theory compactified to four dimensions is often described in terms of an effective supergravity which generically develops classical flat directions. Understanding the leading corrections from string loops and non-perturbative effects is therefore crucial for addressing questions such as moduli stabilization, supersymmetry breaking or cosmological evolution in these models. Although a non-perturbative description of String Theory is still far from being at our disposal, the rich network of dualities allows, already at this stage, to make some explicit computations in simple models. Precisely, type I/heterotic S-duality [1] maps stringy instanton effects due to euclidean 1-branes (E1-branes), into string loop effects in a dual heterotic model. Whereas in ten dimensions S-duality is a strong-weak coupling duality, in four dimensions it is manifested as an electric-magnetic duality, making the mapping between both effective theories straightforward. In this contribution we mainly summarize some of the results of [2], where the structure of multi-instanton and string loop corrections in a simple class of models were obtained. Concretely, we consider type I string theory compactified on toroidal orbifolds, and use type I/heterotic S-duality to extract the corrections to the Kähler potential and the gauge kinetic function, coming from string loop and multi-instanton effects associated with N = 2 subsectors of the theory. Additional related material and a more detailed exposition can be found in [2, 3]. A simple way to extract corrections to the Kähler potential, K, and the gauge kinetic function, fa, of the effective theory is to look at the one-loop physical gauge couplings. In a heterotic compactification, these read,