Gauging Isometries on Hyperkahler Cones and Quaternion-Kahler Manifolds

TL;DR

This paper explores the relationship between hyperkahler cones and quaternion-Kahler manifolds, focusing on how isometries and scalar potentials transfer between these structures, with applications to hypermultiplet target spaces.

Contribution

It extends previous work by detailing the descent of isometries, moment maps, and scalar potentials from hyperkahler cones to quaternion-Kahler manifolds, including explicit examples.

Findings

Described how isometries and scalar potentials descend from cones to quaternion-Kahler spaces.

Applied the framework to hypermultiplets with Wolf space target spaces, including the universal hypermultiplet.

Provided explicit gauging procedures and scalar potential computations for these spaces.

Abstract

We extend our previous results on the relation between quaternion-Kahler manifolds and hyperkahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kahler space. As an example of the general construction, we discuss the gauging and the corresponding scalar potential of hypermultiplets with the unitary Wolf spaces as target spaces. This class includes the universal hypermultiplet.