On Singular Fibres in F-Theory

TL;DR

This paper links the singular fibre types in elliptic Calabi-Yau fourfolds with unramified Higgs vevs in field theory models, clarifying their geometric and physical significance in F-theory.

Contribution

It establishes a direct connection between fibre types in fourfolds and Higgs vev ramification, enhancing understanding of F-theory geometries.

Findings

Naively expected fibre types occur only with unramified Higgs vevs.

Linear unramified Higgs vevs produce specific Kodaira fibre types.

Esole-Yau fourfolds are consistent with unramified Higgs vevs, not puzzling.

Abstract

In this paper, we propose a connection between the field theory local model (Katz-Vafa field theory) and the type of singular fibre in flat crepant resolutions of elliptic Calabi-Yau fourfolds, a class of fourfolds considered by Esole and Yau. We review the analysis of degenerate fibres for models with gauge groups SU(5) and SO(10) in detail, and observe that the naively expected fibre type is realized if and only if the Higgs vev in the field theory local model is unramified. To test this idea, we implement a linear (unramified) Higgs vev for the `E6' Yukawa point in a model with gauge group SU(5) and verify that this indeed leads to a fibre of Kodaira type IV*. Based on this observation, we argue i) that the singular fibre types appearing in the fourfolds studied by Esole-Yau are not puzzling at all, (so that this class of fourfolds does not have to be excluded from the candidate of input data of some yet-unknown formulation of F-theory) and ii) that such fourfold geometries also contain more information than just the eigenvalues of the Higgs field vev configuration in the field theory local models.