FROM TYPE IIA BLACK-HOLES TO T-DUAL TYPE IIB D-INSTANTONS IN N=2, D=4SUPERGRAVITY

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 t he special Kahler moduli space of the IIA N = 2 vector multiplets to t he 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-dimen sional 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 c lass of D-instanton solutions in four dimensions which are determined by a set of harmonic functions plus the underlying topological Calabi- Yau data. (C) 1997 Elsevier Science B.V.