Instanton Numbers and Exchange Symmetries in $N=2$ Dual String Pairs

TL;DR

This paper explores instanton numbers in specific Calabi-Yau spaces, revealing their connection to modular forms and discussing how four-dimensional exchange symmetries relate to six-dimensional heterotic string duality.

Contribution

It identifies relationships between instanton numbers and modular form coefficients in a particular Calabi-Yau space and discusses their implications for string dualities.

Findings

Instanton numbers relate to modular form coefficients.

Exchange symmetries connect 4D models to 6D heterotic duality.

Analysis of Calabi-Yau space $WP_{1,1,2,8,12}(24)$.

Abstract

In this note, we comment on Calabi-Yau spaces with Hodge numbers $h_{1,1}=3$ and $h_{2,1}=243$. We focus on the Calabi-Yau space $WP_{1,1,2,8,12}(24)$ and show how some of its instanton numbers are related to coefficients of certain modular forms. We also comment on the relation of four dimensional exchange symmetries in certain $N=2$ dual models to six dimensional heterotic/heterotic string duality.