Abelian symmetries in multi-Higgs-doublet models

TL;DR

This paper develops a method to classify Abelian symmetry groups in multi-Higgs-doublet models, advancing understanding of possible scalar sector symmetries in theories with multiple Higgs fields.

Contribution

It introduces a strategy to identify all Abelian symmetry groups realizable in NHDM scalar potentials, applicable to any number of Higgs doublets.

Findings

Classified Abelian symmetry groups for NHDM.

Provided examples for 3HDM and 4HDM.

Proved general statements valid for any N.

Abstract

Classifying symmetry groups which can be implemented in the scalar sector of a model with $N$ Higgs doublets is a difficult and an unsolved task for $N>2$. Here, we make the first step towards this goal by classifying the Abelian symmetry groups. We describe a strategy that identifies all Abelian groups which can be realized as symmetry groups of the NHDM scalar potential. We give examples of the use of this strategy in 3HDM and 4HDM and prove several statements for arbitrary $N$.