N = 2 type II-heterotic duality and higher-derivative F-terms Original Research Article

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 Fg satisfy the same holomorphic anomaly equations as in the type II case. Moreover we study the leading singularities of Fgʹs 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.