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, $F(g^2N\to 0)\approx -\frac{ \pi^2}{ 6}N^2V_3T^4(1-\frac{ 3}{ 2\pi^2}g^2N)$. Comparison with the strong coupling expansion provides further indication that free energy is a smooth monotonic function of the coupling constant.
Categories: hep-th hep-ph