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

TL;DR

This paper demonstrates the universality of thermodynamic behavior in conformal field theories with AdS duals, extending the Cardy-Verlinde formula to various settings including weak coupling and flat black holes.

Contribution

It introduces a generalized C-function in CFTs with AdS duals and extends the Cardy-Verlinde formula to new regimes and geometries.

Findings

Cardy-Verlinde entropy formula holds at strong coupling with R-charges and scalars.

The generalized C-function varies monotonically with temperature and scalar fields.

The formula applies to N=4 super Yang-Mills at weak coupling and asymptotically flat black holes.

Abstract

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.