0 60 70 15 v 1 1 3 Ju l 2 00 6 DESY 06 - 109 Static forces in d = 2 + 1 SU ( N ) gauge theories

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 2 0 = 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(r) is obtained and an intermediate distance r s is defined via the property c(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 → ∞, is also computed up to 0.7fm. The deviation from Casimir scaling is positive and grows from 0.1% to 1% in that range.