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

Karsch F, Laermann E, Lütgemeier M. Three-dimensional SU(3) gauge theory and the spatial string tension of the (3+1)-dimensional finite temperature SU(3) gauge theory. Physics Letters B. 1995;346(1-2):94-98.We establish a close relation between the spatial string tension of the (3 + 1)-dimensional SU(3) gauge theory at finite temperature (sigma(s)) and the string tension of the 3-dimensional SU(3) gauge theory (sigma(3)) which is similar to what has been found previously for SU(2). We obtain root sigma(3) = (0.554 +/- 0.004) g(3)(2) and root sigma(s) = (0.586 +/- 0.045) g(2) (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 beta-function with Lambda(T) = 0.118(36) T-c