Résumé:

I'll review the current understanding of the low energy effective theory resulting from compactifications of Type II superstrings on Calabi-Yau manifolds. The effective action can be encoded into the metric on a moduli space which is known to receive quantum stringy corrections, both perturbative and non-perturbative. I'll show how the non-perturbative geometry of this moduli space can be described using twistorial techniques. In the end, I'll argue that the instanton effects coming from NS5-branes, whose understanding is still very incomplete, might be related to a quantization of a certain integrable structure.