We investigate the contributions of the Cartan generators in the static potentials for various representations in the framework of the domain model of center vortices for SU(3) gauge theory. Using the center domains with the cores corresponding to only one Cartan generator [Formula: see text], already given as a particular proposal, leads to some concavities in the potentials for higher representations. Furthermore, the string tension of the fundamental representation is the same at Casimir scaling and [Formula: see text]-ality regimes. We add the contribution of the other Cartan generator [Formula: see text] to the potentials and therefore these shortcomings can be eliminated. However, we discuss that at intermediate range of distances the potentials induced by only [Formula: see text] agree with the Casimir scaling better than those corresponding to both Cartan generators.

中文翻译：

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Cartan 发生器对静态源之间电位的贡献

我们在 SU(3) 规范理论的中心涡流域模型的框架中研究了 Cartan 发生器在各种表示的静态势中的贡献。使用中心域，其核心仅对应于一个 Cartan 生成器 [公式：参见文本]，已经作为一个特定的提议给出，导致更高表示的潜力存在一些凹度。此外，基本表示的弦张力在 Casimir scaling 和 [Formula: see text]-ality 制度下是相同的。我们将其他 Cartan 生成器 [公式：参见文本] 的贡献添加到势能中，因此可以消除这些缺点。然而，我们讨论了在中等距离范围内，仅由 [公式：