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 F g W 2 g 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 g 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 2 g − 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 conifold singularity is governed by c =1 string theory at the self-dual point.