On the Duality between the Heterotic String and F-Theory in 8 Dimensions

TL;DR

This paper explores the deep mathematical relationship between heterotic string theory on a two-torus and F-Theory on an elliptic K3 surface in 8 dimensions, revealing explicit mappings between their moduli spaces.

Contribution

It provides an explicit map relating the deformation parameters of F-Theory K3 surfaces to heterotic string moduli, enhancing understanding of their duality in 8 dimensions.

Findings

Explicit map between F-Theory and heterotic moduli parameters

Connection between K3 discriminant and Calabi-Yau threefold discriminant

Insights into the duality in the context of unbroken E8 x E8 gauge group

Abstract

In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E8 x E8 gauge group. The explicit map relating the deformation parameters alpha and beta of the F-Theory K3 surface to the moduli T and U of the heterotic torus is found using the close relationship between the K3 discriminant and the discriminant of the Calabi-Yau-threefold X(1,1,2,8,12)[24] in the limit of a large base P1.