The Non-Perturbative O(g6) Contribution to the Free Energy of Hot SU(N) Gauge Theory

Perturbation theory in its original formulation fails beyond O(g5) in the calculation of the free energy density of non-Abelian gauge theories [1]. Very recently Braaten [2] has pointed out that the coefficients of the higher powers in the weak coupling expansion can be determined by invoking non-perturbative information from the effective theory of three-dimensional static magnetic fluctuations. In Ref. [2] a systematic two-step separation of the perturbatively treatable fluctuations from the static magnetic sector has been proposed. In the first step the full (electric and magnetic) static sector is represented by an effective threedimensional theory. In this theory (called EQCD) a massive (mE) adjoint scalar field stands for the screened electric fluctuations. In the second step this theory is matched onto an effective magnetic theory (MQCD) with a separation cut-off ΛM . While the contribution of the non-static and static electric modes to the free energy can be safely calculated perturbatively (expansion parameters are g(T ) and mE/T , respectively), the magnetic sector is still non-perturbative and should be investigated by numerical methods. This was done by simulating SU(3) pure gauge theory in 3 dimensions which is just the MQCD. We also calculated the string tension in this theory and compared it to the 4 dimensional spa-