Conformal field theory and hyperbolic geometry

We examine the correspondence betweeen the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. Considering domain boundaries in critical systems and the invariance of the hyperbolic length allows a new interpretation of the basic equation of conformal covariance. The scale factors gain a physical interpretation. We exhibit a fully factored form for the three-point function. An infinite series of minimal models with limit point [ital c]=[minus]2 is discovered. A correspondence between the anomalous dimension and the angle of certain hyperbolic figures emerges.