On Renormalization Group Flows in Four Dimensions

Details On Renormalization Group Flows in Four Dimensions On Renormalization Group Flows in Four Dimensions

2011-07-20

arxiv.org/abs/1107.3987v2

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 4 figures. v2: references added and minor corrections

Scientific paper

We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is "non-Abelian," and leads to a positive-definite universal contribution to the S-matrix of 2->2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

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