Discrete symmetries in the three-Higgs-doublet model

TL;DR

This paper classifies all finite Higgs-family symmetry groups in the three-Higgs-doublet model using advanced group theory, filling a gap in understanding symmetries beyond the Standard Model.

Contribution

It provides a complete classification of finite symmetry groups in the three-Higgs-doublet model using Burnside's theorem, a novel approach in this context.

Findings

Complete list of finite symmetry groups for 3HDM

Application of Burnside's theorem to physics models

Method applicable to other systems like superconductors

Abstract

N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a pivotal role in shaping the phenomenology of the model, and various symmetry groups have been studied so far. However, in spite of all efforts, the classification of finite Higgs-family symmetry groups realizable in NHDM for any N>2 is still missing. Here, we solve this problem for the three-Higgs-doublet model by making use of Burnside's theorem and other results from pure finite group theory which are rarely exploited in physics. Our method and results can be also used beyond high-energy physics, for example, in study of possible symmetries in three-band superconductors.