A note on T-folds and T3 fibrations

We study stringy modifications of T-3-fibered manifolds, where the fiber undergoes a monodromy in the T-duality group. We determine the fibration data defining such T-folds from a geometric model, by using a map between the duality group and the group of large diffeomorphisms of a four-torus. We describe the monodromies induced around duality defects where such fibrations degenerate and we argue that local solutions receive corrections from the winding sector, dual to the symmetry-breaking modes that correct semi-flat metrics

A note on non-flat points in the SU(5) × U(1)PQ F-theory model

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) × 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 10 5 5 5 couplings