Heterotic/type II triality and instantons on K3

A detailed understanding of instanton effects for half-BPS couplings ispursued in theories with 16 supersymmetries. In particular, we investigate theduality 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 dimensionalversions. We present a remarkably clean quantitative test of the duality at thelevel of $F^4$ couplings, by completely matching a purely one-loop heteroticamplitude to a purely tree-level type II result. The triality of SO(4,4) andseveral other miracles are shown to be crucial for the duality to hold. Exactnon-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 IIAor B on $T^4/Z_2$ is obtained. We also analyze the NS5-brane contributions intype II on $K_3\times T^2$, and predict the value $\mu (N)=\sum_{d|N} (1/d^3)$for the bulk contribution to the index of the NS5-brane world-volume theory on$K_3 \times T^2$.Comment: 52 pages, uses JHEP.cls; v2: minor corrections and 2 refs added. Final version for JHE