Symmetries of the Scalar Sector of Multi-Higgs-Doublet Models

TL;DR

This thesis classifies symmetries in multi-Higgs-doublet models, introduces the concept of frustrated symmetries, and presents algorithms for identifying possible Abelian symmetries, including those relevant for dark matter stability.

Contribution

It provides a comprehensive classification of scalar sector symmetries in NHDM, including frustrated symmetries and an algorithmic approach for Abelian symmetry groups.

Findings

Certain symmetries are always broken in models with more than two doublets.

An algorithmic strategy for listing Abelian symmetries in NHDM.

Multi-Higgs models can naturally host dark matter candidates protected by p groups.

Abstract

Classifying the symmetries of the scalar sector in multi-Higgs-doublet models is the main focus of this thesis. We have found certain symmetries that are always broken in models with more than two doublets, which we name "frustrated symmetries". In the attempt towards the classification of possible symmetries in the scalar sector of the NHDM, we find that these symmetry groups are either subgroups of the maximal torus, or certain finite Abelian groups which are not subgroups of maximal tori. For the subgroups of the maximal torus, we present an algorithmic strategy that gives the full list of possible realizable Abelian symmetries for any given $N$. We extend this strategy to include Abelian antiunitary symmetries (with generalized CP transformations) in NHDM. We also show that multi-Higgs-doublet models can naturally accommodate scalar dark matter candidates protected by the group $\Z_p$, since these groups are realizable in NHDM. These models do not require any significant fine-tuning and can lead to a variety of forms of microscopic dynamics among the dark matter candidates.