Static forces in d=2+1 SU(N) gauge theories

Abstract

Using a three-level algorithm we perform a high-precision lattice computation of the static force up to 1fm in the 2+1 dimensional SU(5) gauge theory. Discretization errors and the continuum limit are discussed in detail. By comparison with existing SU(2) and SU(3) data it is found that σr_0^2=1.65-π/24 holds at an accuracy of 1% for all N>=2, where r_0 is the Sommer reference scale. The effective central charge c_{eff}(r) is obtained and an intermediate distance r_s is defined via the property c_{eff}(r_s)=π/24. It separates in a natural way the short-distance regime governed by perturbation theory from the long-distance regime described by an effective string theory. The ratio r_s/r_0 decreases significantly from SU(2) to SU(3) to SU(5), where r_s < r_0. We give a preliminary estimate of its value in the large-N limit. The static force in the smallest representation of N-ality 2, which tends to the k=2 string tension as r->oo, is also computed up to 0.7fm. The deviation from Casimir scaling is positive and grows from 0.1% to 1% in that range.

arXiv comment25 pages, 8 figures, 11 tables

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• Continuum limit of string formation in 3-d SU(2) LGT
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• Disentangling the gravity dual of Yang-Mills theory
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• Strings in SU(N) gauge theories in 2+1 dimensions: beyond the fundamental representation
• Subleading properties of the QCD flux-tube in 3-d lattice gauge theory
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