Geometric minimization of highly symmetric potentials

Understand

In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials.

• Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the usual method.
• By construction, it gives the global minimum for any set of free parameters of the potential, thus offering an intuitive understanding of how they affect the vacuum expectation values.
• For illustration, we apply this method to the S_4 and A_4-symmetric three-Higgs-doublet models.