Superconformal hypermultiplets Original Research Article

We present theories of N=2 hypermultiplets in four space-time dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional special hyper-Kähler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics which itself are Sp(1) fibrations over quaternionic manifolds. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp(n)×Sp(1) bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-Kähler and quaternionic manifolds.