Hypermultiplets, hyperKähler cones and quaternion-Kähler geometry

Abstract

We study hyperkähler cones and their corresponding quaternion-Kähler spaces. We present a classification of 4(n − 1)-dimensional quaternion- Kähler spaces with n abelian quaternionic isometries, based on dualizing superconformal tensor multiplets. These manifolds characterize the geometry of the hypermultiplet sector of classical and perturbative moduli spaces of type-II strings compactified on a Calabi-Yau manifold. As an example of our construction, we study the universal hypermultiplet in detail, and give three inequivalent tensor multiplet descriptions. We also comment on the construction of quaternion-Kähler manifolds that may describe instanton corrections to the moduli space.