The free energy of N=4 super Yang-Mills and the AdS/CFT correspondence

We compute the high-temperature limit of the free energy for four-dimension al N = 4 supersymmetric SU(N-c) Yang-Mills theory. At weak coupling we do s o for a general ultrastatic background spacetime, and in the presence of sl owly-varying background gauge fields. Using Maldacena's conjectured duality , we calculate the strong-coupling large-N-c expression for the special cas e that the three-space has constant curvature. We compare the two results p aying particular attention to curvature corrections to the leading order ex pressions.