The Cardy-Verlinde formula for 2D gravity

TL;DR

This paper extends the relation between the Friedmann equation and the Cardy formula to two-dimensional gravity, highlighting the role of scale symmetry and linking the central charge to Newton's constant.

Contribution

It introduces a two-dimensional version of the Cardy-Verlinde formula, connecting 2D cosmology, entropy bounds, and conformal field theory parameters.

Findings

The relation c=6/G links the central charge to Newton's constant in 2D.

Scale symmetry is essential for defining entropy bounds in 2D cosmology.

The Friedmann equation can be expressed via the Cardy formula in two dimensions.

Abstract

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.