Towards the classification of conformal field theories in arbitrary even dimension

I identify the class of even-dimensional conformal field theories that is m ost similar to two-dimensional conformal field theory. In this class the fo rmula, elaborated recently, for the irreversibility of the renormalization- group flow applies also to massive flows. This implies a prediction for the ratio between the coefficient of the Euler density in the trace anomaly (c harge a) and the stress-tenser two-point function (charge c). More precisel y, the tract anomaly in external gravity is quadratic in the Ricci tensor a nd the Ricci scalar and contains a unique central charge. 1 check the predi ction in detail in four, six and eight dimensions, and then in arbitrary ev en dimension. (C) 2000 Published by Elsevier Science B.V. All rights reserv ed.