New extended superconformal sigma models and quaternion Kahler manifolds

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 M-H(4(n + 1)) of dimension 4(n + 1) from a 2n-dimensional real analytic Kahler-Hodge manifold M-K(2n). The latter emerges as a maximal Kahler submanifold of the 4n-dimensional quaternion Kahler space M-Q(4n) such that its Swann bundle coincides with M-H(4)(n + 1). 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.