Conditions for global minimum in the $$A_4$$ A 4 symmetric 3HDM

Abstract

Abstract There has been a great interest in three Higgs doublet models (3HDM) symmetric under an exact $$A_4$$ A 4 symmetry. We provide the complete analytic necessary and sufficient conditions for a point to be the global minimum along the neutral directions in such models, discussing many of the subtleties involved. We also present a number of numerical examples, to highlight those issues. We then turn to the directions which break electric charge, presenting a safe analytical sufficient condition for bounded from below (BFB) potentials. Based on extensive numerical simulations, we discuss one conjecture on BFB along charge breaking directions.