F-Theory on Calabi-Yau Fourfolds

TL;DR

This paper explores F-theory compactifications on elliptically fibered Calabi-Yau fourfolds, examining their geometric properties and dualities with heterotic strings, supported by Hodge number calculations.

Contribution

It introduces a class of Calabi-Yau fourfolds with elliptic and K3 fibrations and provides numerical evidence for F-theory dualities in four dimensions.

Findings

Identification of a simple class of fourfolds with elliptic and K3 fibrations

Calculation of Hodge numbers supporting F-theory/heterotic duality

Numerical evidence for dualities in four-dimensional F-theory

Abstract

We discuss some aspects of F-theory in four dimensions on elliptically fibered Calabi-Yau fourfolds which are Calabi-Yau threefold fibrations. A particularly simple class of such manifolds emerges for fourfolds in which the generic Calabi-Yau threefold fiber is itself an elliptic fibration and is K3 fibered. Duality between F-theory compactified on Calabi-Yau fourfolds and heterotic strings on Calabi-Yau threefolds puts constraints on the cohomology of the fourfold. By computing the Hodge diamond of Calabi-Yau fourfolds we provide first numerical evidence for F-theory dualities in four dimensions.