N = 2 Type I-heterotic duality and higher derivative F-terms

We test the conjectured Type I-heterotic duality in four dimensions by analyzing a given class of higher derivative F-terms of the form FgW2g, with W the N = 2 gravitational superfield. We study a particular dual pair of theories, the O(2,2) heterotic model and a type I model based on the K3Z2 orbifold theory constructed by Gimon and Polchinski, further compactified on a torus. The Fg couplings appear at 1-loop on both theories; because of the weak-weak nature of this duality in four dimensions, it is meaningful to compare the heterotic Fgʹs with the corresponding type 1 couplings perturbatively. We compute the Fgʹs in type I, showing that they receive contributions only from N = 2 BPS states and that in the appropriate limit they coincide with the heterotic coupling, in agreement with the given duality.