Heterotic/Type II Triality and Instantons on $K_3$

TL;DR

This paper explores dualities between heterotic and type II string theories on K3 surfaces, providing exact instanton effects, matching amplitudes, and new non-perturbative results, enhancing understanding of supersymmetric couplings.

Contribution

It offers a precise test of heterotic/type II duality at the level of F^4 couplings and derives new non-perturbative instanton contributions on K3 surfaces.

Findings

Complete matching of heterotic one-loop and type II tree-level amplitudes.

Exact non-perturbative results for various string theories on K3.

Prediction of NS5-brane index contributions on K3 times T^2.

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 $K_3 \times T^2$.