The geometry of hypermultiplets

TL;DR

This paper reviews the geometry of hypermultiplets in supergravity and string theory, focusing on quaternion-Kähler manifolds and their relevance to the swampland, highlighting specific examples of swampland QK-manifolds.

Contribution

It provides a concise overview of hypermultiplet moduli spaces and explores quaternion-Kähler geometries in the context of the swampland, including concrete examples.

Findings

Hypermultiplet target spaces are quaternion-Kähler manifolds of negative scalar curvature.

Certain quaternion-Kähler manifolds are identified as belonging to the swampland.

The review connects hypermultiplet geometry with string theory and swampland constraints.

Abstract

This is a light and short review on the geometry of hypermultiplets coupled to supergravity and its appearance in string theory. As is long known, the target space of the hypermultiplet sigma-model is a quaternion-K\"ahler (QK) manifold of negative scalar curvature. We review some aspects of hypermultiplet moduli spaces, but also study aspects of QK-geometries in relation to the swampland, including some concrete examples of swampland QK-manifolds.