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 element 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.
Journal of High Energy Physics
- Pub Date:
- December 2011
- Spontaneous Symmetry Breaking;
- Renormalization Group;
- High Energy Physics - Theory
- 24 pages, 4 figures. v2: references added and minor corrections