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arXiv · 2605.07651

Conditions for boundedness from below of a $\Delta(54)$-symmetric three-Higgs-doublet model

Darius Jurčiukonis·Luís Lavoura
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Abstract

We investigate the orbit space of the scalar potential of a $\Delta(54)$-symmetric three-Higgs-doublet model. We find that, if the potential enjoys $CP$ invariance, then its three-dimensional orbit space is a polytope; if the potential has no $CP$ symmetry, then its four-dimensional orbit space has a boundary that is sometimes slightly concave, but seems never to be convex. Consequently, we conjecture necessary and sufficient conditions for the potential to be bounded from below; brute-force minimization of a large number of potentials affirms the accuracy of our conjecture. We list all possible charge-conserving and charge-breaking minima of the potential.

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Darius Jurčiukonis, Luís Lavoura. 2026-05-08. Conditions for boundedness from below of a $\Delta(54)$-symmetric three-Higgs-doublet model. https://arxiv.org/abs/2605.07651

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