Superconformal Hypermultiplets

TL;DR

This paper develops theories of N=2 hypermultiplets in four dimensions that are invariant under superconformal symmetries, describing their target spaces as special hyper-K"ahler and quaternionic manifolds with a flexible formulation.

Contribution

It introduces a general formulation of superconformal hypermultiplet theories using local bundle sections, accommodating arbitrary coordinate choices on hyper-K"ahler and quaternionic manifolds.

Findings

Characterization of target spaces as cones over tri-Sasakian metrics.

Formulation of Lagrangian and transformation rules with bundle sections.

Application to hypermultiplet coupling in N=2 supergravity.

Abstract

We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special} hyper-K\"ahler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics and are locally the product of a flat four-dimensional space and a quaternionic manifold. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp$(n)\times{\rm Sp}(1)$ bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-K\"ahler and quaternionic manifolds.