Three-dimensional SU (3) gauge theory and the spatial string tension of the (3+1)-dimensional finite temperature SU (3) gauge theory

We establish a close relation between the spatial string tension of the 3-dimensional SU (3) gauge theory at finite temperature (σs) and the string tension of the 3-dimensional SU (3) gauge theory (σ3) which is similar to what has been found previously for SU (2). We obtain δ3=(0.554±0.004)g23 and> δ5=(0.586 ± 0.045)g2(T)T, respectively. For temperatures larger than twice the critical temperature, results are consistent with a temperature dependent coupling running according to the two-loop β-function with ΛT = 0.118(36)Tc.