Duality of N=2 Heterotic -- Type I Compactifications in Four Dimensions

TL;DR

The paper addresses Type I -- heterotic duality in four-dimensional $N=2$ theories arising from the Coulomb phase of a six-dimensional $U(16)$ orientifold compactified on $T^2$. It develops and compares the perturbative prepotentials, Kahler potentials, gauge threshold corrections, and the full tower of higher-derivative $F_g$ couplings in the weak-coupling limits, showing precise agreement between the Type I and heterotic descriptions when the moduli map $S\leftrightarrow S', U\leftrightarrow U$ and $T\leftrightarrow S'$ is applied. On the Type I side, the couplings are controlled by the spectrum of N=2 BPS states arising from D=6 massless modes, while on the heterotic side they are calculated from torus amplitudes and lattice sums, with duality translating tree-level and loop contributions between the two pictures. The results establish a comprehensive match of both holomorphic and non-holomorphic couplings across the dual pair, including the infinite set of higher-derivative interactions ${\cal F}_g W^{2g}$, and thus provide strong evidence for the non-perturbative Type I -- heterotic duality in this four-dimensional setting.

Abstract

We discuss type I -- heterotic duality in four-dimensional models obtained as a Coulomb phase of the six-dimensional U(16) orientifold model compactified on T^2 with arbitrary SU(16) Wilson lines. We show that Kahler potentials, gauge threshold corrections and the infinite tower of higher derivative F-terms agree in the limit that corresponds to weak coupling, large T^2 heterotic compactifications. On the type I side, all these quantities are completely determined by the spectrum of N=2 BPS states that originate from D=6 massless superstring modes.