Scale Invariance and Conformal Invariance
Jean-Francois Fortin (CERN)

We investigate the theoretical implications of scale without conformal invariance in quantum field theory. We argue that RG flows of such theories correspond to recurrent behaviors, i.e. limit cycles or ergodicity, and show how dilatation generators do generate dilatations. We discuss the implications for the a-theorem, and use Weyl consistency conditions to show that scale implies conformal invariance. Finally, we clarify the necessary and sufficient conditions for conformality and present new types of conformal field theories.