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

Abstract

We establish a close relation between the spatial string tension of the (3+1)-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 σ = ( 0.554 ± 0.004 ) g 3 2 and σ = ( 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 β-function with Aτ = 0.118(36)Tc.