CFT, holography, and causal entropy bound

The causal entropy bound (CEB) is confronted with recent explicit entropy calculations in weakly and strongly coupled conformal field theories (CFTs) in arbitrary dimension D. For CFTs with a large number of fields, N, the CEB is found to be valid for temperatures not exceeding a value of order MP/N1D−2, in agreement with large N bounds in generic cut-off theories of gravity, and with the generalized second law. It is also shown that for a large class of models including high-temperature weakly coupled CFTs and strongly coupled CFTs with AdS duals, the CEB, despite the fact that it relates extensive quantities, is equivalent to (a generalization of) a purely holographic entropy bound proposed by E. Verlinde.