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

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