Dftt 17/98 a Proof of the Irreversibility of Renormalization Group Flows in Four Dimensions

We present a proof of the irreversibility of renormalization group flows, i.e. the c–theorem for unitary, renormalizable theories in four (or generally even) dimensions. Using Ward identities for scale transformations and spectral representation arguments, we show that the c–function based on the trace of the energy-momentum tensor (originally suggested by Cardy) decreases monotonically along renormalization group trajectories. At fixed points this c–function is stationary and coincides with the coefficient of the Euler density in the trace anomaly, while away from fixed points its decrease is due to the decoupling of positive–norm massive modes. Submitted to: Nuclear Physics B