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

Abstract : 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 $T^4$ 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 $K_3 \\times T^2$.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00016312
Contributor : Boris Pioline Connect in order to contact the contributor
Submitted on : Monday, December 26, 2005 - 4:26:59 PM
Last modification on : Tuesday, November 16, 2021 - 4:54:26 AM

### Citation

E. Kiritsis, N. A. Obers, B. Pioline. Heterotic/Type II Triality and Instantons on $K_3$. Journal of High Energy Physics, Springer, 2000, 0001, pp.029. ⟨hal-00016312⟩

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