Hypermultiplets, hyperKähler cones and quaternion-Kähler geometry

Abstract

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