D-instantons and Universal Hypermultiplet

The quantum non-perturbative geometry of the toy model of the universal hyper-multiplet is discussed. We consider the simple case when the D-instantons, originating from the Calabi-Yau wrapped D2-branes, preserve a U(1) × U(1) symmetry of the universal hypermultiplet moduli space. Our aim is to find some quaternionic solutions to the effective NLSM metric of the universal hypermultiplet, which would interpolate between the perturbative (large CY volume) region and the superconfor-mal (Landau-Ginzburg) region. Given the unbroken local N=2 supersymmetry and the U(1) × U(1) isometry of the universal hypermultiplet moduli space, the cluster decomposition of D-instantons is proved to be valid in a curved spacetime too. We also calculate the non-perturbative scalar potential in the hyper-Kähler limit, when an abelian isometry of the universal hypermultiplet moduli space is gauged in the presence of D-instantons.