Properties of the general NHDM. II. Higgs potential and its symmetries

TL;DR

This paper develops a geometric approach to analyze the Higgs potential in N-Higgs-doublet models, focusing on symmetries and global minima without explicit calculations, with applications to three-Higgs-doublet variants.

Contribution

It introduces a geometric technique for studying the Higgs potential's global minimum and symmetry patterns in NHDM, extending analysis without explicit minimization.

Findings

Developed a geometric method to analyze the Higgs potential

Identified symmetry patterns in NHDM potentials

Applied the method to specific three-Higgs-doublet models

Abstract

We continue our analysis of the general N-Higgs-doublet model and focus of the Higgs potential description in the space of gauge orbits. We develop a geometric technique that allows us to study the global minimum of the potential without explicitly finding its position. We discuss symmetry patterns of the NHDM potential, and illustrate the general discussion with various specific variants of the three-Higgs-doublet model.