Effective field theory program for conformal quantum anomalies

The emergence of conformal states is established for any problem involving a domain of scales where the long-range SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs is in place, this renormalization mechanism is capable of producing binding in the strong-coupling regime. A realization of this phenomenon, in the form of dipole-bound anions, is discussed.