  Hypermultiplet couplings in type IIA string theory on a Calabi-Yau space can
be quantum corrected by D2-brane instantons wrapping special Lagrangian cycles.
On the other hand, hypermultiplet couplings in the heterotic string on a K3
surface are corrected by world-sheet instantons wrapping curves. In a class of
examples, we relate these two sets of instanton corrections. We first present
an analogue of the c-map for the heterotic string via a dual flux
compactification of M-theory. Using this duality, we propose two ways of
capturing quantum corrections to hypermultiplets. We then use the orientifold
limit of certain F-theory compactifications to relate curves in K3 to special
Lagrangians in dual type IIA compactifications. We conclude with some results
from perturbative string theory for hypermultiplet F-terms and a conjecture
about the topology of brane instantons.
