Scale Anomalies, States, and Rates in Conformal Field Theory

<!--HTML-->Scale anomalies are present in conformal field theory very much like in any other quantum field theory. The anomaly coefficients in a CFT are numbers, known to "count the degrees of freedom" of the theory. This talk discusses new methods that make this statement more precise, and shows how the scale anomaly coefficients can be computed in terms of the CFT data in arbitrary dimension. An important tool developed along the way is the definition of a complete set of CFT states in Minkowski momentum space. Positivity of the scale anomaly coefficients follows from the optical theorem. (based on arXiv:1612.07800)