Homogeneous linear intrinsic constraints in the stationary manifold of a GG-invariant potential

Jun 12, 2023
25 pages
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20212022202302
Abstract: (arXiv)
Given a GG-invariant potential V\mathcal{V} of a scalar multiplet φ\varphi, there may exist a set of homogenous linear equations that constrain the components of a stationary point of V\mathcal{V} independently of the coefficients of the terms in V\mathcal{V}. We call them homogeneous linear intrinsic constraints (HLICs). HLICs in a stationary point manifest as HLICs in the corresponding vacuum alignment of φ\varphi, which plays a central role in predictive phenomenological models. We discover that a group H~\tilde{H} generates HLICs if the terms in V\mathcal{V} satisfy a condition, which we call the compatibility condition. In this paper, we also develop a procedure, which involves splitting V\mathcal{V} into smaller parts, to establish the existence of specific stationary points using arguments based on symmetries without the need for explicitly extremizing the potential. Using this procedure, we obtain H~\tilde{H} as a direct product of the symmetry groups associated with the various irreducible multiplets (irreps) in φ\varphi. This results from considering the potentials of the irreps separately and verifying if the cross terms are compatible with H~\tilde{H}.
Note:
  • multiplet: scalar
  • stability
  • buildings
  • splitting
  • alignment
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