Comment on two loop free energy in N=4 supersymmetric Yang-Mills theory at finite temperature

The strong coupling behavior of finite temperature free energy in N = 4 supersymmetric SU(N) Yang-Mills theory has been recently discussed by Gubser, Klebanov and Tseytlin in the context of AdS-SYM correspondence. In this note, we focus on the weak coupling behavior. As a result of a two-loop computation we obtain, in the large N ’t Hooft limit, F(g 2 N ! 0) � π 2