From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity

We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N=2, D=4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N=2 vector multiplets to the quaternionic moduli space of the N=2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kahler effective action, into IIB D-instanton solutions of the IIB quaternionic sigma-model action, where the D-instantons can be obtained by compactifying odd IIB D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determinded by a set of harmonic functions plus the underlying topological Calabi-Yau data.