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 generall y even) dimensions. Using Ward identities for scale transformations and spe ctral representation arguments, we show that the c-function based on the tr ace of the energy-momentum tensor (originally suggested by Cardy) decreases monotonically along renormalization group trajectories. At fixed points th is 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. (C) 1998 Elsevier Sc ience B.V.