Geometrical Aspects of Fivebranes in Heterotic/F-Theory Duality in Four Dimensions

TL;DR

This paper investigates the geometry of Calabi-Yau fourfolds in F-theory/heterotic duality, focusing on fivebranes and their degenerations, to understand non-perturbative effects in four-dimensional compactifications.

Contribution

It introduces a method to analyze degenerations of fourfolds related to fivebranes, revealing new geometric structures and criteria for superpotential generation.

Findings

Degenerations of fourfolds correspond to fivebrane configurations.

Certain degenerations can be described via base degenerations of elliptic fibrations.

Witten's criterion identifies which fivebranes generate superpotentials.

Abstract

We use the method of stable degenerations to study the local geometry of Calabi-Yau fourfolds for F-theory compactifications dual to heterotic compactifications on a Calabi-Yau threefold with fivebranes wrapping holomorphic curves in the threefold. When fivebranes wrap intersecting curves, or when many fivebranes wrap the same curve, the dual fourfolds degenerate in interesting ways. We find that some of these can be usefully described in terms of degenerations of the base of the elliptic fibrations of these fourfolds. We use Witten's criterion to determine which of the fivebranes can lead to the generation of a non-perturbative superpotential.