Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2006-07-13
Nucl.Phys.B758:204-226,2006
Physics
High Energy Physics
High Energy Physics - Lattice
25 pages, 8 figures, 11 tables
Scientific paper
10.1016/j.nuclphysb.2006.09.027
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 \sigma r_0^2=1.65-\pi/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)=\pi/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.
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