Compactifications of F-Theory on Calabi--Yau Threefolds -- I

TL;DR

This paper explores F-theory compactifications on Calabi-Yau threefolds, revealing how certain dualities in string theory are geometrically realized and providing insights into strong coupling transitions.

Contribution

It demonstrates the promotion of 4D N=2 dualities to 6D N=1 dualities and shows how heterotic dualities become geometric symmetries in F-theory.

Findings

N=2 dualities become N=1 dualities in 6D

Heterotic/heterotic duality is a geometric symmetry

Insights into strong coupling transitions in heterotic strings

Abstract

We study compactifications of F-theory on certain Calabi--Yau threefolds. We find that $N=2$ dualities of type II/heterotic strings in 4 dimensions get promoted to $N=1$ dualities between heterotic string and F-theory in 6 dimensions. The six dimensional heterotic/heterotic duality becomes a classical geometric symmetry of the Calabi--Yau in the F-theory setup. Moreover the F-theory compactification sheds light on the nature of the strong coupling transition and what lies beyond the transition at finite values of heterotic string coupling constant.