Superconformal hypermultiplets

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-Kahler 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) x Sp(1) bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-Kahler and quaternionic manifolds. (C) 2000 Elsevier Science B.V. All rights reserved.