We exploit the 6D, \( \mathcal{N} \) = (1, 0) and \( \mathcal{N} \) = (1, 1) harmonic superspace approaches to construct the full set of the maximally supersymmetric on-shell invariants of the canonical dimension d = 12 in 6D, \( \mathcal{N} \) = (1, 1) supersymmetric Yang-Mills (SYM) theory. Both single- and double-trace invariants are derived. Only four single-trace and two double-trace invariants prove to be independent. The invariants constructed can provide the possible counterterms of \( \mathcal{N} \) = (1, 1) SYM theory at four-loop order, where the first double-trace divergences are expected to appear. We explicitly exhibit the gauge sector of all invariants in terms of \( \mathcal{N} \) = (1, 0) gauge superfields and find the absence of \( \mathcal{N} \) = (1, 1) supercompletion of the F⁶ term in the abelian limit.

我们利用 6 D, \( \mathcal{N} \) = (1 , 0) 和\( \mathcal{N} \) = (1 , 1) 谐波超空间方法来构造全集的最大超对称-shell 不变量的规范维度d = 12 in 6 D, \( \mathcal{N} \) = (1 , 1) 超对称 Yang-Mills (SYM) 理论。导出单迹和双迹不变量。只有四个单迹和两个双迹不变量被证明是独立的。构造的不变量可以提供\( \mathcal{N} \) = (1 ,1) 四环顺序的 SYM 理论，其中预计会出现第一个双迹发散。我们根据\( \mathcal{N} \) = (1 , 0) 规范超场明确展示了所有不变量的规范扇区，并发现\( \mathcal{N} \) = (1 , 1) 超完成的缺失阿贝尔极限中的F ⁶项。