Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry

TL;DR

This paper classifies certain quaternion-Kahler spaces with abelian isometries using hyperkahler cones and superconformal tensor multiplets, with applications to string theory moduli spaces.

Contribution

It provides a new classification of quaternion-Kahler spaces with abelian isometries derived from hyperkahler cones and superconformal methods, including explicit examples.

Findings

Classified 4(n-1)-dimensional quaternion-Kahler spaces with n abelian isometries.

Presented multiple tensor multiplet descriptions of the universal hypermultiplet.

Discussed potential quaternion-Kahler manifolds for instanton corrections.

Abstract

We study hyperkahler cones and their corresponding quaternion-Kahler spaces. We present a classification of 4(n-1)-dimensional quaternion-Kahler spaces with n abelian quaternionic isometries, based on dualizing superconformal tensor multiplets. These manifolds characterize the geometry of the hypermultiplet sector of 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-Kahler manifolds that may describe instanton corrections to the moduli space.