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.