New extended superconformal sigma models and Quaternion Kahler manifolds

TL;DR

This paper introduces a new projective-superspace method to construct hyperkahler cones from Kahler-Hodge manifolds, advancing the explicit generation of quaternion Kahler metrics relevant for supergravity theories.

Contribution

It presents a novel construction linking Kahler-Hodge manifolds to hyperkahler cones via projective superspace, enriching the toolkit for building quaternion Kahler spaces.

Findings

Constructed hyperkahler cones from Kahler-Hodge manifolds.

Provided a method for explicit quaternion Kahler metric generation.

Potential applications in supergravity reduction and embedding.

Abstract

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