Heterotic/type-II triality and instantons on K-3

A detailed understanding of instanton effects for half-BPS couplings is pur sued in theories with 16 supersymmetries. In particular, we investigate the duality between heterotic string on T-4 and type-IIA on K-3 at the T-4/Z(2 ) orbifold point, as well as their higher and lower dimensional versions. W e present a remarkably clean quantitative test of the duality at the level of F-4 couplings, by completely matching a purely one-loop heterotic amplit ude to a purely tree-level type-II result. The triality of SO(4, 4) and sev eral other miracles are shown to be crucial for the duality to hold. Exact non-perturbative new results for type I', F on K-3, M on K-3, and IIB on K- 3 are found, and the general form of D-instanton contributions in type IIA or B on T-4/Z(2) is obtained. We also analyze the NS5-brane contributions i n type II on K-3 x T-2, and predict the value mu (N) = Sigma (d/N) (1/d(3)) for the bulk contribution to the index of the NS5-brane world-volume theor y on K-3 x T-2.