Instanton sums and five-dimensional gauge theories

We analyze the vector multiplet prepotential of d = 4, N = 2 type IIA compactifications. We find that the world-sheet instanton corrections have a natural interpretation as one-loop corrections in five dimensions, with the extra dimension compactified on a circle of radius g_sℓ _s. We argue that the relation between space-time and world-sheet instantons is natural from this point of view. We also discuss the map between the type IIA world-sheet instantons and the space-time instantons in the heterotic dual.