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

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

1998-05-04

arxiv.org/abs/hep-th/9805015v2

Nucl.Phys. B535 (1998) 709-728

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/S0550-3213(98)00631-2

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.

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