The hypermultiplet moduli space of compactified type IIA string theory.
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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.