2009/06/24 by Sergei M. Kuzenko, Ulf Lindström, Ulf Lindstrom +1 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/09/119
published as JHEP 0909:119,2009 · 30 pages
arxiv created 2009/06/24 · openalex publication_date 2009/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quaternion Kahler manifolds are known to be the target spaces for matter hypermultiplets coupled to N=2 supergravity. It is also known that there is a one-to-one correspondence between 4n-dimensional quaternion Kahler manifolds and those 4(n+1)-dimensional hyperkahler spaces which are the target spaces for rigid superconformal hypermultiplets (such spaces are called hyperkahler cones). In this paper we present a projective-superspace construction to generate a hyperkahler cone M4(n+1)H of dimension 4(n+1) from a 2n-dimensional real analytic Kahler-Hodge manifold M2nK. The latter emerges as a maximal Kahler submanifold of the 4n-dimensional quaternion Kahler space M4nQ such that its Swann bundle coincides with M4(n+1)H. Our approach should be useful for the explicit construction of new quaternion Kahler metrics. The results obtained are also of interest, e.g., in the context of supergravity reduction N=2 --> N=1, or alternatively from the point of view of embedding N=1 matter-coupled supergravity into an N=2 theory.