The Hypermultiplet with Heisenberg Isometry in N=2 Global and Local Supersymmetry

TL;DR

This paper explores the structure of hypermultiplets with Heisenberg symmetry in N=2 supersymmetry, linking global and local cases, and characterizes the perturbative corrections in string compactifications.

Contribution

It explicitly constructs the connection between global and local supersymmetry for hypermultiplets with Heisenberg isometry, including a gravity decoupling limit in string theory.

Findings

Reduced scalar manifolds to a one-parameter family with perturbative corrections

Established the link between hyper-Kaehler and quaternion-Kaehler geometries

Provided a gravity decoupling limit in perturbative string theory

Abstract

The string coupling of N=2 supersymmetric compactifications of type II string theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hypermultiplet, that has four real scalars living on a quaternion-Kaehler manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of perturbative isometries, reduces the possible manifolds to a one-parameter family that describes the tree-level effective action deformed by the only possible perturbative correction arising at one-loop level. A similar argument can be made at the level of global supersymmetry where the scalar manifold is hyper-Kaehler. In this work, the connection between global and local supersymmetry is explicitly constructed, providing a non-trivial gravity decoupled limit of type II strings already in perturbation theory.