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arXiv · 0710.3490

Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology

I. P. Ivanov
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Abstract

We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of non-contractible paths in the Higgs orbit space. We also study explicit symmetries of the Higgs potential/lagrangian and their spontaneous violation from a wider perspective than usual.

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I. P. Ivanov. 2007-10-18. Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology. https://doi.org/10.1103/physrevd.77.015017

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