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 1 fm in the (2+1)-dimensional SU(5) gauge theory. The Sommer parameter r0=0.5fm is used to set the scale. Discretization errors and the continuum limit are discussed in detail. By comparison with existing SU(2) and SU(3) data it is found that σr02=1.65−π24 holds at an accuracy of 1% for all N⩾2. The effective central charge c(r) is obtained and an intermediate distance rs is defined via the property c(rs)=π24. 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 rs/r0 decreases significantly from SU(2) to SU(3) to SU(5), where rs