Complete set of bounded-from-below conditions for the $A_4$-symmetric three-Higgs-doublet model

Abstract

We derive bounded-from-below necessary conditions for the scalar potential of an $A_4$-invariant three-Higgs-doublet model. The field Ansätze that we have used were devised with the help of Claude. Testing our set of conditions on $10^6$ random potentials, that in parallel we minimize by brute force using the Mathematica package StableWein, we find that the set seems to be necessary and sufficient for boundedness-from-below.