String tensions in deformed Yang-Mills theory

Abstract

We study k-strings in deformed Yang-Mills (dYM) with SU(N) gauge group in the semiclassically calculable regime on ${\mathrm{I}\mathrm{R}}^3\times S^1$. 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.

v3: To be published version, 78 pages, 7 figures, Added extended discussion of non-commutativity of large N and large area limits

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• Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
• Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
• Entanglement entropy, dualities, and deconfinement in gauge theories
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• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
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