From Type IIA black holes to T-dual Type IIB D-instantons in N = 2, D = 4 supergravity

Abstract

We discuss the T-duality between the solutions of type 11A 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 Kähler 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 Kähler effective action, into IIB D-instanton solutions of the IIB quaternionic σ-model action, where the D-instantons can be obtained by compactifying odd 1113 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 determined by a set of harmonic functions plus the underlying topological Calabi-Yau data.