  Two dimensional conformal field theories, can be described by their pseudo
Goldstone bosons when the conformal symmetry is spontaneously and anomalously
broken. We show that the Schwarzian action of these bosons leads to the Cardy
formula without using modular invariance. As a result, the Cardy formula
applies to conformal field theories on a cylinder and chiral theories in one
dimension. This also explains why the Cardy--Verlinde formula for theories on
$S^1 \times S^{d-2}$ can be written in the form of the Cardy formula of an
effective two dimensional theory.
