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# Stability of the embedded string in the $SU(N)\times U(1)$ Higgs model and its application

Mar 2023

Since it has been pointed out that physics beyond the Standard Model may beconstrained by gravitational waves from cosmic strings, it has been moreimportant to clarify in what cases cosmic strings are formed. We study thestability of the embedded string which is formed when $SU(N)\times U(1)_X$gauge symmetries are broken to $SU(N-1)\times U(1)_Q$, and find that thestability condition can be determined by two mass ratios of the Higgs andmassive gauge bosons, and does not explicitly depend on $N$. We also show thatthe result can be extended in supersymmetric models. In addition, we applythese results to several models and discuss the important feature of the Higgsto produce the embedded string. Although we find it difficult to be satisfiedin normal realistic GUT models, it is possible if $SU(N)$ and $U(1)_X$ havedifferent origins.

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