$A_4$ Family Symmetry from SU(5) SUSY GUTs in 6d

TL;DR

This paper presents a novel 6D orbifold SU(5) SUSY GUT model where $A_4$ family symmetry naturally emerges, explaining quark and lepton masses, mixing angles, and neutrino oscillations.

Contribution

It introduces the first model combining orbifold GUTs with $A_4$ family symmetry derived from orbifolding, addressing fermion mass hierarchies and mixing.

Findings

Achieves realistic quark and lepton mass matrices

Reproduces tri-bimaximal neutrino mixing

Provides a mechanism for inter-family mass hierarchy

Abstract

We propose a model in which $A_4$ Family Symmetry arises dynamically from a six dimensional orbifold SU(5) Supersymmetric Grand Unified Theory. The SU(5) is broken to the Standard Model gauge group by a particular orbifold compactification leading to $A_4$ Family Symmetry, low energy Supersymmetry and Higgs doublet-triplet splitting. The resulting four dimensional effective superpotential leads to a realistic description of quark and lepton masses and mixing angles including tri-bimaximal neutrino mixing and an inter-family mass hierarchy provided by a Froggatt-Nielsen mechanism. This model is the first which combines the idea of orbifold GUTs with $A_4$ family symmetry resulting from the orbifolding.