N=2 Type II- Heterotic duality and Higher derivative F-terms

TL;DR

This paper tests N=2 Type II–heterotic duality by examining higher-derivative F-terms $F_g W^{2g}$, showing Type II contributions arise at genus $g$ as topological partition functions, while the heterotic side yields these at one loop. In a rank-$3$ example, the authors prove that the holomorphic anomaly equations for $F_g$ match between dual theories in the large-$S$ limit, and they analyze the leading singularities near enhanced symmetry points, finding universal coefficients linked to the Euler numbers of genus-$g$ moduli spaces. They connect these leading singularities to the $c=1$ string at the self-dual radius and provide explicit one-loop calculations in the heterotic theory to support the conjectured duality. The work offers strong evidence for duality across loop orders, suggests a universal conifold description, and outlines future directions for higher-order corrections and extensions to other ranks. Overall, the results substantiate a deep interplay between Type II and heterotic descriptions in four-dimensional $N=2$ theories and illuminate the non-perturbative structure of higher-derivative couplings.

Abstract

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 $F_g W^{2g}$ 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 $2g{-}2$ 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 conifold singularity is governed by $c{=}1$ string theory at the self-dual point.