Heterotic / type II triality and instantons on K(3)

A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with 16 supersymmetries. In particular, we investigate the duality between heterotic string on T4 and type-IIA on K3 at the T4/2 orbifold point, as well as their higher and lower dimensional versions. We present a remarkably clean quantitative test of the duality at the level of F4 couplings, by completely matching a purely one-loop heterotic amplitude to a purely tree-level type-II result. The triality of SO(4,4) and several other miracles are shown to be crucial for the duality to hold. Exact non-perturbative new results for type I', F on K3, M on K3, and IIB on K3 are found, and the general form of D-instanton contributions in type IIA or B on T4/2 is obtained. We also analyze the NS5-brane contributions in type II on K3 × T2, and predict the value μ(N) = ∑d|N(1/d3) for the bulk contribution to the index of the NS5-brane world-volume theory on K3 × T2.