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 CFT's with a large number of fields, N, the CEB
is found to be valid for temperatures not exceeding a value of order
MP/ND−21, 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 CFT's and
strongly coupled CFT's 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.Comment: 14 pages, 2 figure