Perturbative Couplings and Modular Forms in N=2 String Models with a Wilson Line

TL;DR

This paper analyzes four-parameter N=2 string models from heterotic and type II perspectives, using modular forms to compute key couplings and verifying dualities through instanton number comparisons.

Contribution

It introduces a method to compute the perturbative prepotential and gravitational couplings using generalized modular forms in N=2 string models.

Findings

Computed perturbative prepotential and F1 couplings using modular forms.

Verified heterotic/type II duality via instanton number matching.

Connected results to recent theoretical proposals.

Abstract

We consider a class of four parameter D=4, N=2 string models, namely heterotic strings compactified on K3 times T2 together with their dual type II partners on Calabi-Yau three-folds. With the help of generalized modular forms (such as Siegel and Jacobi forms), we compute the perturbative prepotential and the perturbative Wilsonian gravitational coupling F1 for each of the models in this class. We check heterotic/type II duality for one of the models by relating the modular forms in the heterotic description to the known instanton numbers in the type II description. We comment on the relation of our results to recent proposals for closely related models.