Three-Dimensional SU(3) gauge theory and the Spatial String Tension of the (3+1)-Dimensional Finite Temperature SU(3) Gauge Theory

TL;DR

This paper explores the relationship between the spatial string tension in finite-temperature (3+1)-dimensional SU(3) gauge theory and the string tension in a 3-dimensional SU(3) gauge theory, providing quantitative links and temperature-dependent behavior.

Contribution

It establishes a quantitative relation between the spatial string tension in (3+1)D and the string tension in 3D SU(3) gauge theory, extending previous SU(2) results.

Findings

Derived numerical values for $\sigma_3$ and $\sigma_s$

Confirmed temperature dependence of the coupling via two-loop $eta$-function

Results consistent for temperatures above twice the critical temperature

Abstract

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 $\sqrt{\sigma_3} = (0.554 \pm 0.004) g_3^2$ and $\sqrt{\sigma_s} = (0.586 \pm 0.045)g^2(T) T$, 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 $\Lambda_T = 0.118(36)T_c$.