Universality and a generalized C-function in CFTs with AdS duals

We argue that the thermodynamics of conformal field theories with AdS duals exhibits a remarkable universality. At strong coupling, a Cardy-Verlinde entropy formula holds even when R-charges or bulk supergravity scalars are turned on. In such a setting, the Casimir entropy can be identified with a generalized C-function that changes monotonically with temperature as well as when non-trivial bulk scalar fields are introduced. We generalize the Cardy-Verlinde formula to cases where no subextensive part of the energy is present and further observe that such a formula is valid for the N = 4 super Yang-Mills theory in D = 4 even at weak coupling. Finally we show that a generalized Cardy-Verlinde formula holds for asymptotically flat black holes in any dimension. (C) 2002 Elsevier Science B.V. All rights reserved.