Fivebrane instantons in Calabi-Yau compactifications

We provide the last missing piece of the complete non-perturbative description of the low energy effective action emerging from Calabi-Yau compactifications of type II string theory — NS5-brane instanton corrections to the hypermultiplet moduli space $M_H$. We find them using S-duality symmetry of the type IIB formulation. The result is encoded in a set of holomorphic functions on the twistor space of $M_H$ and includes all orders of the instanton expansion.