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Discrete symmetries in the three-Higgs-doublet model

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arxiv 1206.7108 v2 pith:FEP2PH7Z submitted 2012-06-29 hep-ph math.GR

Discrete symmetries in the three-Higgs-doublet model

I. P. Ivanov , E. Vdovin This is my paper
classification hep-ph math.GR
keywords modelnhdmsymmetriessymmetrybeyonddiscretefinitegroups
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Hilbert Series and the Flavor Invariants of the 3HDM

    hep-th 2026-04 conditional novelty 6.0

    The full multigraded Hilbert series of the 3HDM is computed in closed form, and a basis of SU(3)-invariant operators is constructed up to cubic order in the quartic couplings.

  2. Systematic analysis of 3HDM symmetries

    hep-ph 2025-12 conditional novelty 6.0

    A systematic catalogue of realisable Higgs-family, general-CP, and GOOFy/T-GOOFy symmetries in three-Higgs-doublet models, with new invariant potentials and a corrected U(1)◦V4 group structure.

  3. The Hilbert Series and the Flavor Invariants of the 3HDM

    hep-th 2026-04 unverdicted novelty 4.0

    Hilbert series for 3HDM global symmetries is computed with explicit invariants constructed up to cubic order.