The hypermultiplet moduli space of compactified type IIA string theory.

Abstract

We have looked at the hypermultiplet moduli space of the effective supergravity theory obtained from type IIA superstring theory compactified on a Calabi-Yau manifold. It is possible to give this space hypermultiplet moduli space a more intrinsic description as a fibre bundle over the moduli space of deformations of the Calabi-Yau manifold used in the compactification procedure. The fibres may can be interpreted as the symplectised spaces for a compact quotient of the Heisenberg group constructed from the (Weil) intermediate Jacobian of the Calabi-Yau manifold and viewed as a contact manifold. We use the complex structure on the Weil intermediate Jacobian to define a Sasakian (contact metric) structure on this Heisenberg group that can be extended to a metric on the fibres.