Modular Family Symmetry in F-Theory GUTs from the Bottom-up

Finite modular family symmetry can emerge from top-down approaches based on heterotic string theory or Type IIB string theory. We show that, in addition to such approaches, it can also emerge from local F-Theory bottom-up constructions. As a first example of the new approach, we have analysed in detail a concrete F-Theory Fluxed $SU(5)$ Grand Unified Theory (GUT) with modular S₄ family symmetry. The model fits the fermion mass and mixing data very well and serves as a demonstration of the bottom-up approach to modular family symmetry in F-Theory fluxed GUTs.