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) × 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.
Highlights
Model which was already studied in [13,14,15], and follow-up works, and which we review in detail below
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
Our main result is that in the weak coupling limit these non-flat points do not interfere with the desirable GUT-physics, so they are harmless for model building purposes
Summary
We review and extend the analysis of the global F-theory realisation of the SU(5) × U(1) Peccei-Quinn model [15], cf. [13, 14] for the local description along the GUT-divisor. If we assume for the above fibration a two-dimensional base the so-obtained Calabi-Yau threefold will be Q-factorial with terminal singularity points Such varieties have recently been studied from the F-theory perspective in [16, 22]. This hints already at a four-point coupling 1035−15−15−1 but to get a better picture of what really happens at these points, we have to look at the full fourfold geometry, especially the fibre structure As it turns out, these are points where the dimension of the resolved fibre jumps, i.e. the fibration described by (2.5) and (2.6) over a three-dimensional (or higher dimensional) base is non-flat.. A summary of the curves and the coupling points of this setup is depict in figure 1
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