  We study the rigid limit of a class of hypermultiplet moduli spaces appearing
in Calabi-Yau compactifications of type IIB string theory, which is induced by
a local limit of the Calabi-Yau. We show that the resulting hyperkahler
manifold is obtained by performing a hyperkahler quotient of the Swann bundle
over the moduli space, along the isometries arising in the limit. Physically,
this manifold appears as the target space of the non-linear sigma model
obtained by compactification of a five-dimensional gauge theory on a torus.
This allows to compute dyonic and stringy instantons of the gauge theory from
the known results on D-instantons in string theory. Besides, we formulate a
simple condition on the existence of a non-trivial local limit in terms of
intersection numbers of the Calabi-Yau, and find an explicit form for the
hypermultiplet metric including corrections from all mutually non-local
D-instantons, which can be of independent interest.
