Superconformal hypermultiplets

We present theories of N = 2 hypermultiplets in four space-time dimensions that are invariant under rigid or local superconformal symmetries. The targ et spaces of theories with rigid superconformal invariance are (4n)-dimensi onal special hyper-Kahler manifolds. Such manifolds can be described as con es over tri-Sasakian metrics which itself are Sp(1) fibrations over quatern ionic manifolds. The latter manifolds appear in the coupling of hypermultip lets to N = 2 supergravity. We employ local sections of an Sp(n) x Sp(1) bu ndle in the formulation of the Lagrangian and transformation rules, thus al lowing for arbitrary coordinatizations of the hyper-Kahler and quaternionic manifolds. (C) 2000 Elsevier Science B.V. All rights reserved.