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

TL;DR

This paper investigates the dependence of $k$-strings in pure Yang-Mills theory on representation N-ality using supersymmetry, revealing non-universal corrections and the deconfinement of W-bosons on the string worldsheet.

Contribution

It introduces a novel approach connecting super Yang-Mills and pure Yang-Mills to analyze $k$-strings, highlighting non-universal correction terms and the behavior of W-bosons.

Findings

Next-to-leading order corrections depend on permutation group characters.

W-bosons are deconfined on the string worldsheet, not affecting N-ality.

Comparison with other theories and holographic models.

Abstract

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.