String tensions in deformed Yang-Mills theory

TL;DR

This paper investigates the tensions of k-strings in deformed Yang-Mills theory, revealing that their ratios do not follow traditional scaling laws but are bounded by a square root of Casimir scaling, with implications for understanding confinement.

Contribution

It provides the first detailed numerical and analytical study of k-string tensions in deformed Yang-Mills theory, highlighting deviations from known scaling laws and connecting to the Bag Model.

Findings

k-string ratios do not obey sine- or Casimir-scaling

Ratios are bounded above by a square root of Casimir scaling

Large-N k-strings in dYM do not become free

Abstract

We study k-strings in deformed Yang-Mills (dYM) with SU(N) gauge group in the semiclassically calculable regime on ${\rm I\!R}^3 \times S^1$. Their tensions T$_{\text{k}}$ are computed in two ways: numerically, for $2$ $\le$ N $\le$ $10$, and via an analytic approach using a re-summed perturbative expansion. The latter serves both as a consistency check on the numerical results and as a tool to analytically study the large-N limit. We find that dYM k-string ratios T$_{\text{k}}$/T$_{\text{1}}$ do not obey the well-known sine- or Casimir-scaling laws. Instead, we show that the ratios T$_{\text{k}}$/T$_{\text{1}}$ are bound above by a square root of Casimir scaling, previously found to hold for stringlike solutions of the MIT Bag Model. The reason behind this similarity is that dYM dynamically realizes, in a theoretically controlled setting, the main model assumptions of the Bag Model. We also compare confining strings in dYM and in other four-dimensional theories with abelian confinement, notably Seiberg-Witten theory, and show that the unbroken $Z_N$ center symmetry in dYM leads to different properties of k-strings in the two theories; for example, a "baryon vertex" exists in dYM but not in softly-broken Seiberg-Witten theory. Our results also indicate that, at large values of N, k-strings in dYM do not become free.