The para-HK/QK correspondence

TL;DR

This paper extends the hyper-Kahler/quaternionic Kahler correspondence to para-geometries, providing a new proof of the quaternionic Kahler nature of the target manifold and constructing deformations of supergravity metrics.

Contribution

It introduces a para-geometric generalization of the HK/QK correspondence and proves the quaternionic Kahler property of the target manifold in this broader context.

Findings

The target manifold of the HK/QK correspondence is quaternionic Kahler.

Constructed one-parameter deformations of supergravity c-map metrics.

Deformations are shown to be para-quaternionic Kahler.

Abstract

We generalise the hyper-Kahler/quaternionic Kahler (HK/QK) correspondence to include para-geometries, and present a new concise proof that the target manifold of the HK/QK correspondence is quaternionic Kahler. As an application, we construct one-parameter deformations of the temporal and Euclidean supergravity c-map metrics and show that they are para-quaternionic Kahler.