# Spontaneous breaking of SO(3) to finite family symmetries with supersymmetry — an *A*_{4} model

## Abstract

We discuss the breaking of SO(3) down to finite family symmetries such as *A*_{4}, *S*_{4} and *A*_{5} using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric *A*_{4} and its finite subgroups *Z*_{3} and *Z*_{2}. We then propose a supersymmetric *A*_{4} model of leptons along these lines, originating from SO(3) × U(1), which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged SO(3), leading to massive gauge bosons, and show that all domain wall problems are resolved in this model.

## Keywords

Gauge Symmetry Discrete Symmetries Neutrino Physics Supersymmetric Effective Theories## Notes

### **Open Access**

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