Geometry of the scalar couplings in N=2 supergravity models

Abstract

The author describes the quaternionic geometry of various sigma -model target spaces for the hypermultiplet couplings in four-dimensional N=2 conformal and Poincare supergravity models. The process of eliminating the non-physical superconformal gauge fields of chiral SU(2) and dilations is examined in the context of the quaternionic associated bundle. The sigma -model target space X parametrized by the scalar fields of the hypermultiplets in an N=2 conformal supergravity-matter Lagrangian is shown to be the quaternionic associated bundle of the sigma -model quaternionic Kahler target space M of the corresponding N=2 Poincare supergravity-matter system. The manifold X is special hyperKahler manifold with an isomeric SU(2) action rotating the hyperKahler structure and M can be obtained as a certain SU(2) reduction of X. This suggests possible generalizations of the superconformal tensor calculus and the Lagrangian constructed by de Wit et al (1985). The quaternionic Kahler join and some new matter couplings are also discussed.