The hypermultiplet with Heisenberg isometry in N = 2 global and local supersymmetry

Abstract

The string coupling of N = 2 supersymmetric compactifications of type IIstring theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hypermultiplet,that has four real scalars living on a quaternion-Kähler manifold. RequiringHeisenberg symmetry, which is a maximal subgroup of perturbative isometries, reducesthe possible manifolds to a one-parameter family that describes the tree-level effective actiondeformed by the only possible perturbative correction arising at one-loop level. Asimilar argument can be made at the level of global supersymmetry where the scalar manifoldis hyper-Kähler. In this work, the connection between global and local supersymmetryis explicitly constructed, providing a non-trivial gravity decoupled limit of type II stringsalready in perturbation theory. © SISSA 2011.