arXiv:hep-th/9611017v2 10 Jan 1997 SISSA-159/96/EP N =2 Type I-Heterotic Duality and Higher Derivative F-Terms Marco Serone International School for Advanced Studies, ISAS-SISSA Via Beirut n. 2-4, 34013 Trieste, Italy and Istituto Nazionale di Fisica Nucleare, sez. di Trieste, Italy e-mail:serone@sissa.it Abstract We test the conjectured Type I-Heterotic Duality in four dimensions by analyzing a given class of higher derivative F-terms of the form F g W 2g , 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 K3 Z 2 orbifold theory constructed by Gimon and Polchinski, further compactified on a torus. The F g 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 F g ’s with the corresponding type I couplings perturbatively. We compute the F g ’s 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 couplings, in agreement with the given duality. PACS: 11.25.Mj Keywords: F-terms, Strings, N=2, Duality