Abstract :
Some instanton corrections to the universal hypermultiplet moduli space metric of the type IIA string theory compactified on a Calabi–Yau threefold arise due to multiple wrapping of BPS membranes and five-branes around certain cycles of Calabi–Yau. The classical universal hypermultipet metric is locally equivalent to the Bergmann metric of the symmetric quaternionic space SU(2,1)/U(2), whereas its generic quaternionic deformations are governed by the integrable SU(∞) Toda equation. We calculate the exact (non-perturbative) UH metrics in the special cases of (i) the D-instantons (the wrapped D2-branes) in the absence of five-branes, and (ii) the five-brane instantons with vanishing charges, in the absence of D-instantons. The solutions of the first type preserve the U(1)×U(1) classical symmetry, while they can be interpreted as the gravitational dressing of the hyper-Kähler D-instanton solutions. The solutions of the second type preserve the non-abelian SU(2) classical symmetry, while they can be interpreted as the gradient flows in the universal hypermultiplet moduli space.
