Exact thresholds and instanton effects in string theory

In this lecture we summarize some recent work on the understanding of insta nton effects in string theories with 16 supersymmetries. In particular, we consider F-4 couplings using the duality between the heterotic string on T- 4 and type IIA on K-3 at an orbifold point, as well as higher and lower dim ensional versions of this string-string duality. At the perturbative level a non-trivial test of the duality, requiring several miraculous identities, is presented by matching a purely one-loop heterotic amplitude to a purely tree-level type II result. A wide variety of non-perturbative effects is s hown to occur in this setting, including D-brane instantons for type IIA on K-3 X S-1 and NS5-brane instantons for type IIA on K-3 x T-2 Moreover, the analysis of the three-dimensional case, which possesses a non-perturbative SO(8, 24, Z) U-duality, reveals the presence of Kaluza-Klein 5-brane insta nton effects, both on the heterotic and the type II side.