Modular Family Symmetry in Fluxed GUTs

TL;DR

This paper explores how modular family symmetries, specifically an $S_4$ symmetry, can influence Yukawa couplings in fluxed GUT models inspired by F-theory, providing a new perspective on flavor structure in particle physics.

Contribution

It introduces a novel framework linking modular family symmetries to fluxed GUTs, with detailed analysis of an $SU(5)$ model exhibiting $S_4$ symmetry.

Findings

Yukawa couplings depend on complex structure moduli as modular forms.

Demonstrates the application of $S_4$ symmetry in fluxed GUTs.

Provides a concrete example of modular symmetry in F-theory inspired models.

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.