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The emergence of conformal states is established for any problem involving adomain of scales where the long-range, SO(2,1) conformally invariantinteraction is applicable. Whenever a clear-cut separation of ultraviolet andinfrared cutoffs is in place, this renormalization mechanism produces bindingin the strong-coupling regime. A realization of this phenomenon, in the form ofdipole-bound anions, is discussed.Comment: 15 pages. Expanded, with additional calculational details. To be  published in Phys. Rev.

Effective field theory program for conformal quantum anomalies