Gauging isometries on hyperKahler cones and quaternion Kahler manifolds

We extend our previous results on the relation between quaternion-Kähler manifolds and hyperk¨ahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kähler 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