R-symmetry constants in $mathcal{N}=4$ SYM in Yukawa terms

The expression for $mathcal{N}=4$ SYM in the Lorentz covariant form involves structure constants of $SU(4)$ R-symmetry group in the Yukawa terms (formula 3.1 from here https://arxiv.org/abs/hep-th/0201253):
$$
g C_{i}^{ab} lambda_{a} [X^{i}, lambda_{b}]
+
g bar{C}_{iab} bar{lambda}^{a} [X^{i}, bar{lambda}^{b}]
$$
And these structure constants are said to originate straightforwardly from the dimensional reduction of $mathcal{N}=1$ SYM from 10d to 4d.

However, there are no such constants in Van der Waerden notation (dotted/undotted), as shown in this paper – https://arxiv.org/abs/1001.3871:
$$
phi_{ij} {chi_{alpha}^{i}, chi^{j alpha}} + phi_{ij} {chi_{dot{alpha}}^{i}, chi^{j dot{alpha}}}
$$
Here $alpha, dot{alpha}$ are the spinor indices.
The raise and lowering of the $R$-symmetry indices, if I am not mistaken is performed via $varepsilon$-symbol, and It seems so far not evident, that this structure constant can be so easily absorbed.
Where have the structure constants gone?