On discrete Twist and Four-Flux in N=1 heterotic/F-theory compactifications

TL;DR

This paper investigates the duality between N=1 heterotic string and F-theory, focusing on the relationship between four-flux and discrete twist, supported by detailed Euler number computations for singular Calabi-Yau fourfolds.

Contribution

It provides an indirect argument for the flux-twist matching in heterotic/F-theory duality, including detailed Euler number calculations for singular geometries.

Findings

Confirmed the flux-twist relation $G^2=- au_* eta^2$ in specific compactifications.

Performed detailed Euler number computations for singular Calabi-Yau fourfolds.

Supported the duality correspondence through geometric and topological analysis.

Abstract

We give an indirect argument for the matching $G^2=-\pi_* \gamma^2$ of four-flux and discrete twist in the duality between N=1 heterotic string and $F$-theory. This treats in detail the Euler number computation for the physically relevant case of a Calabi-Yau fourfold with singularities.