A Note on Non-Flat Points in the $SU(5)\times U(1)$ PQ F-Theory Model

TL;DR

This paper investigates non-flat fibrations in an $SU(5) imes U(1)$ F-theory model, revealing their role in generating higher order couplings in the effective superpotential, with implications for phenomenology.

Contribution

It provides the first detailed analysis of non-flat fibers in a global $SU(5) imes U(1)$ F-theory model and links them to specific higher order couplings.

Findings

Non-flat fibers correspond to higher order superpotential couplings.

Identifies a specific $ extbf{10} extbf{5} extbf{5} extbf{5}$ coupling.

Supports the interpretation of non-flat fibers as physical effects.

Abstract

Non-flat fibrations often appear in F-theory GUT models, and their interpretation is still somewhat mysterious. In this note we explore this issue in a model of particular phenomenological interest, the global $SU(5)\times U(1)$ Peccei-Quinn F-theory model. We present evidence that co-dimension three non-flat fibres give rise to higher order couplings in the effective four-dimensional superpotential. More specifically, in our example we find $\mathbf{10}\, \mathbf{5}\, \mathbf{5}\, \mathbf{5}$ couplings.