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.

PhD thesis