The color neutrality of hadrons is interpreted as an expression of conformal symmetry of strong interaction, the latter being signaled through the detected "walking" at low transferred momenta, lim Q 2 →0 α s (Q 2 )/π → 1, of the strong coupling toward a fixed value (α s "freezing" ). The fact is that conformal symmetry admits quarks and gluons to reside on the compactified AdS 5 boundary, whose topology is S 1 × S 3 , a closed space that can bear exclusively color-charge neutral configurations, precisely as required by color confinement. The compactification radius, once employed as a second scale alongside with Λ QCD , provides for an α s (Q 2 ) "freezing" mechanism in the infrared regime of QCD, thus making the conformal-symmetry-color-neutrality connection at low energies evident. In this way, perturbative descriptions of processes in the infrared could acquire meaning. In consequence, it becomes possible to address QCD by quantum mechanics in terms of a conformal wave operator equation, which leads to an efficient description of a wide range of data on hadron spectra, electromagnetic form factors, and phase transitions.