Résumé:

I'll review the progress achieved in constructing the non-perturbative hypermultiplet moduli space using twistorial methods. The metric on this space determines the low-energy effective action of Type II string theory compactified on a Calabi-Yau threefold. It receives instanton corrections due to D-branes and NS5-branes and I'll show how all of them can be nicely incorporated at the level of the twistor space. However, so far this construction has provided NS5-instantons only in the one-instanton approximation, so that they represent the last missing piece of the full non-perturbative picture. I'll argue that the inclusion of these corrections may be closely related to quantization of a certain integrable structure.