NHDM势中正则 custodial 对称性的表示论刻画
Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials
AI总结：
该研究基于表示论与几何关系，推导了N>2的N希格斯二重态势中正则SO(4)_C保管对称性的充要条件，并针对N=3、4、5的情况给出了可高效实现的对称性判定算法。
摘要：
通过研究N希格斯二重态势的基协变组分，我们基于表示论与几何关系，推导了二重态数N>2时势的正则SO(4)_C Custodial Symmetry（CS，保管对称性）存在的充要条件。本质上，我们的刻画将正则CS的存在性与对应于正交李代数定义表示特定基的基协变矢量相关联。对于N=3、4、5的情况，这些条件的验证只需极少的计算量，我们还提供了可高效在计算机程序中实现的实用算法，用于判定一个势是否具有保管对称性。
英文摘要：
By considering the basis-covariant constituents of N-Higgs-doublet potentials, we derive necessary and sufficient conditions for canonical SO(4)_C Custodial Symmetry (CS) of potentials with N>2 doublets, based on representation-theoretical and geometrical relations. In essence, our characterization relates the presence of canonical CS to basis-covariant vectors corresponding to particular bases of the defining representation of the orthogonal Lie algebras. For N=3,4 and 5, the conditions demand little computational effort to be evaluated, and we provide practical algorithms that may be efficiently implemented in a computer program, for deciding whether or not a potential is custodial-symmetric.
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