D-instantons and universal hypermultiplet

Quantum non-perturbative geometry of the universal hypermultiplet is investigated. We consider the simple case when the D-instantons, originating from the Calabi-Yau wrapped D2-branes, preserve a U(1)xU(1) symmetry of the universal hypermultiplet moduli space. The cluster decomposition of D-instantons is proved to be valid in a curved spacetime. We find an SL(2,Z) duality-invariant quaternionic solution to the effective NLSM metric of the universal hypermultiplet, which is governed by a modular-invariant function. This function appears to be the same function found by Green and Gutperle, and describing the modular invariant completion of the R^4 term by the D-instanton effects in the type-II superstring/M-theory. We argue that our solution interpolates between the perturbative (large CY volume) region and the superconformal (Landau-Ginzburg) region in the universal hypermultiplet moduli space. We also calculate a non-perturbative scalar potential in the hyper-K\"ahler limit, when an abelian isometry of the universal hypermultiplet moduli space is gauged in the presence of D-instantons.