A proof of the irreversibility of renormalization group flows in four dimensions

Abstract

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.

22 pages, 2 figures, plain tex with harvmac and epsf; several typos corrected; final version, to be published in Nucl. Phys. B

References in corpus (1)

• C Function Representation of the Local Potential Approximation

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