On the representation (in)dependence of $k$-strings in pure Yang-Mills theory via supersymmetry

We exploit a conjectured continuity between super Yang-Mills on $\mathbb R^3\times \mathbb S^1$ and pure Yang-Mills to study $k$-strings in the latter theory. As expected, we find that Wilson-loop correlation functions depend on the N-ality of a representation ${\cal R}$ to the leading order. However, the next-to-leading order correction is not universal and is given by the group characters, in the representation ${\cal R}$, of the permutation group. We also study W-bosons in super Yang-Mills and show that they are deconfined on the string worldsheet, and therefore, can change neither the string N-ality nor its tension. This phenomenon mirrors the fact that soft gluons do not screen probe charges with non-zero N-ality in pure Yang-Mills. Finally, we comment on the scaling law of $k$-strings in super Yang-Mills and compare our findings with strings in Seiberg-Witten theory, deformed Yang-Mills theory, and holographic studies that were performed in the 't Hooft large-$N$ limit.