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

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 $10555$ couplings.

26 pages. v2: Revised version to appear in JHEP. v3: Additional discussion in the conclusions