The Cardy–Verlinde formula for 2D gravity

We discuss the different bounds on entropy in the context of two-dimensional cosmology. We show that in order to obtain well definite bounds one has to use the scale symmetry of the gravitational theory. We then extend the recently found relation between the Friedmann equation and the Cardy formula to the case of two dimensions. In particular, we find that in two dimensions this relation requires that the central charge c of the conformal field theory is given in terms of the Newton constant G of the gravitational theory by c=6/G.