Hypermultiplets and topological strings

The c-map relates classical hypermultiplet moduli spaces in compactificationsof type II strings on a Calabi-Yau threefold to vector multiplet moduli spacesvia a further compactification on a circle. We give an off-shell description ofthe c-map in N=2 superspace. The superspace Lagrangian for the hypermultipletsis a single function directly related to the prepotential of special geometry,and can therefore be computed using topological string theory. Similarly, aclass of higher derivative terms for hypermultiplets can be computed from thehigher genus topological string amplitudes. Our results provide a framework forstudying quantum corrections to the hypermultiplet moduli space, as well as forunderstanding the black hole wave-function as a function of the hypermultipletmoduli.Comment: 21 pages, references adde