Minima of multi-Higgs potentials with triplets of $\Delta(3n^2)$ and $\Delta(6n^2)$

Abstract

We analyse the minima of scalar potentials for multi-Higgs models where the scalars are arranged as either one triplet or two triplets of the discrete symmetries $A_4$, $S_4$, $\Delta(27)$, $\Delta(54)$, as well as $\Delta(3n^2)$ and $\Delta(6n^2)$ with $n>3$. The results should be useful for both multi-Higgs models involving electroweak doublets and multi-flavon models involving electroweak singlets, where in both cases the fields transform as triplets under some non-Abelian discrete symmetry.