Conifold singularities, resumming instantons and non-perturbative mirror symmetry

We determine the instanton corrected hypermultiplet moduli space in type IIB compactifications near a Calabi-Yau conifold point where the size of a two-cycle shrinks to zero. We show that D1-instantons resolve the conifold singularity caused by world sheet instantons. Furthermore, by resumming the instanton series,were produce exactly the results obtained by Ooguri and Vafa on the type II A side, where membrane instantons correct the hypermultiplet moduli space. Our calculations therefore establish that mirror symmetry holds non-perturbatively in the string coupling.