Discrete Family Symmetry from F-Theory GUTs

TL;DR

This paper explores how discrete family symmetries like $A_4$ and $S_3$ naturally emerge from F-theory GUT models, providing explicit calculations and analyzing their implications for fermion masses and neutrino data.

Contribution

It offers an explicit F-theory-based derivation of discrete family symmetries from monodromies, connecting geometric properties to phenomenological models.

Findings

Discrete symmetries arise from monodromies in F-theory.

Analysis of polynomial discriminants links geometry to family symmetries.

Proposes a discrete doublet-triplet splitting mechanism.

Abstract

We consider realistic F-theory GUT models based on discrete family symmetries $A_4$ and $S_3$, combined with $SU(5)$ GUT, comparing our results to existing field theory models based on these groups. We provide an explicit calculation to support the emergence of the family symmetry from the discrete monodromies arising in F-theory. We work within the spectral cover picture where in the present context the discrete symmetries are associated to monodromies among the roots of a five degree polynomial and hence constitute a subgroup of the $S_5$ permutation symmetry. We focus on the cases of $A_4$ and $S_3$ subgroups, motivated by successful phenomenological models interpreting the fermion mass hierarchy and in particular the neutrino data. More precisely, we study the implications on the effective field theories by analysing the relevant discriminants and the topological properties of the polynomial coefficients, while we propose a discrete version of the doublet-triplet splitting mechanism.