1999/09/30 by Bernard de Wit, Bas Kleijn, B. Kleijn +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Geometry #Geometry and complex manifolds #Homogeneous space #Invariant (physics) #Kähler manifold #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Supergravity #Supersymmetry #Transformation (genetics) #hep-th
paper · pdf · doi:10.1016/s0550-3213(99)00726-9
published as Nucl.Phys.B568:475-502,2000 · 30 pages
arxiv created 1999/09/30 · openalex publication_date 2000/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional \it special hyper-Kähler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics and are locally the product of a flat four-dimensional space and a quaternionic manifold. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp(n)×\rm Sp(1) bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-Kähler and quaternionic manifolds.