On the Mathematical Limitations and Physical Relevance of the F-theory Landscape

It is shown that a generic point in the complex structure moduli space of elliptically fibered Calabi-Yau 4-folds does not possess any gauge symmetry. Consequently, gauge symmetry does not arise generically in the F-theory landscape at the purely geometric level, implying that the appearance of gauge symmetry requires highly non-generic tuning of moduli. Mathematical analysis further indicates that the geometry-physics correspondence underlying the F-theory framework possesses intrinsic mathematical limitations.