N=4 supersymmetric Yang-Mills thermodynamics from effective field theory

The free energy density of $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions is derived through second order the 't Hooft coupling $\ensuremath{\lambda}$ at finite temperature using effective-field methods. contributions to this come from hard scale $T$ and soft $\sqrt{\ensuremath{\lambda}}T$. effects are encoded coefficients an effective three-dimensional field that obtained by dimensional reduction temperature. electric $\sqrt{\ensuremath{\lambda}}T$ taken into account perturbative calculations theory.