N=2 TYPE-II HETEROTIC DUALITY AND HIGHER-DERIVATIVE F-TERMS

We test the recently conjectured duality between N = 2 supersymmetric type II and heterotic string models by analysing a class of higher-dimensional interactions in the respective low-energy Lagrangians. These are F-terms of the form FgW2g where W is the gravitational superfield. On the type II side these terms are generated at the g-loop level and in fact are given by topological partition functions of the twisted Calabi-Yau sigma model. We show that on the heterotic side these terms arise at the one-loop level. We study in detail a rank-3 example and show that the corresponding couplings F, satisfy the same holomorphic anomaly equations as in the type II case. Moreover we study the leading singularities of F-g's on the heterotic side, near the enhanced symmetry point and show that they are universal poles of order 2g - 2 with coefficients that are given by the Euler number of the moduli space of genus-g Riemann surfaces. This confirms a recent conjecture that the physics near the conifold singularity is governed by c = 1 string theory at the self-dual point.