Gravitational dressing of D-instantons

The non-perturbative corrections to the universal hypermultiplet moduli space metric in the type-IIA superstring compactification on a Calabi–Yau threefold are investigated in the presence of 4d, N=2 supergravity. These corrections come from multiple wrapping of the BPS (Euclidean) D2-branes around certain (BPS) Calabi–Yau 3-cycles, and they are known as the D-instantons. The exact universal hypermultiplet metric is governed by a quaternionic potential that satisfies the SU(∞) Toda equation. When the supergravity decouples, the metric is hyper-Kähler. We propose the mechanism that gravitationally dress any (D-instanton) hyper-Kähler metric to the (universal hypermultiplet) quaternionic metric of the same dimension.