Modular Family Symmetry in Fluxed GUTs

Abstract: We discuss modular family symmetry in effective theories based on generic properties of bottom-up local F-theory inspired GUTs broken by fluxes, which we refer to as Fluxed GUTs. We argue that the Yukawa couplings will depend on the complex structure moduli of the matter curves in such a way that they can be modular forms associated with these symmetries. To illustrate the approach we analyse in detail a concrete local fluxed $SU(5)$ GUT with modular $S_4$ family symmetry.