Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach

TL;DR

This paper explores how to derive finite non-Abelian discrete family symmetries like A4 and Delta(27) from an underlying SU(3) gauge symmetry through spontaneous symmetry breaking, focusing on vacuum alignments and potentials.

Contribution

It introduces a systematic approach for obtaining finite family symmetries from SU(3) by using higher irreducible representations and analyzing symmetry breaking potentials.

Findings

Methods for identifying vacuum alignments are presented.

Explicit symmetry breaking potentials are discussed in detail.

Finite family symmetries can be derived from SU(3) gauge symmetry.

Abstract

Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying SU(3) gauge symmetry. Higher irreducible representations are required to achieve the spontaneous breaking of the continuous group. We present methods of identifying the required vacuum alignments and discuss in detail the symmetry breaking potentials.