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## Heterotic/Type II Triality and Instantons on $K_3$

### Abstract

52 pages, uses JHEP.cls; v2: minor corrections and 2 refs added. Final version for JHEPA 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 $T^4$ and type IIA on $K_3$ at the $T^4/Z_2$ orbifold point, as well as their higher and lower dimensional versions. We present a remarkably clean quantitative test of the duality at the level of $F^4$ 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 $K_3$, 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 in type 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 $K_3 \\times T^2$

Topics: [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]
Publisher: Springer
Year: 2000
OAI identifier: oai:HAL:hal-00016312v1
Provided by: Hal-Diderot