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.
We construct explicit complete Ricci-flat metrics on the total spaces of certain vector bundles over flag manifolds of the group SU (n), for all Kähler classes. These metrics are natural generalizations of the metrics of Candelas-de la Ossa on the conifold, Pando Zayas-Tseytlin on the canonical bundle over CP 1 × CP 1 , as well as the metrics on canonical bundles over flag manifolds, recently constructed by van Coevering.
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 Tfolds 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. arXiv:1803.00550v1 [hep-th]
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