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

TL;DR

This paper tests the duality between N=2 supersymmetric type II and heterotic string models by analyzing higher derivative F-terms, confirming their equivalence and revealing universal singularity behavior near conifold points.

Contribution

It demonstrates the matching of higher derivative F-terms in dual models and explores their singularity structure, supporting the conjectured duality.

Findings

F-terms are generated at g-loop in type II and one-loop in heterotic models.

Couplings satisfy the same holomorphic anomaly equations in both models.

Singularities near enhanced symmetry points are universal poles with coefficients related to Euler numbers.

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.