Judging from these results, we infer that the actual β function of QCD will interpolate between the nonperturbative results for Q < 1 GeV and the pQCD results for Q > 1 GeV. We also observe that the general conditions β ( Q → 0) = β ( Q → ∞ ) = 0 , (13) β ( Q ) < 0 , for Q > 0 , (14) dβ dQ ∣ Q = Q 0 = 0 , (15) dβ dQ < 0 , for Q < Q$_{0}$, dβ dQ > 0 , for Q > Q$_{0}$. (16) are satisfied by our model β function obtained from LF holography. Equation (13) expresses the fact that QCD approaches a conformal theory in both the far ultraviolet and deep infrared regions. In the semiclassical approximation to QCD without particle creation or absorption, the β function is zero, and the approximate theory is scale invariant in the limit of massless quarks. [46] When quantum corrections are included, the conformal behavior is preserved at very large Q because of asymptotic freedom and near Q → 0 because the theory develops a fixed point. An infrared fixed point is in fact a natural consequence of color confinement: [28] since the propagators of the colored fields have a maximum wavelength, all loop integrals in the computation of the gluon self-energy decouple at Q 2 → 0. [29] Condition (14) for large Q $^{2}$, expresses the basic antiscreening behavior of QCD where the strong coupling vanishes. The β function in QCD is essentially negative, thus the coupling increases monotonically from the UV to the IR where it reaches its maximum value: it has a finite value for a theory with a mass gap. Equation (15) defines the transition region at Q$_{0}$ where the β function has a minimum. Since there is only one hadronic-partonic transition, the minimum is an absolute minimum; thus the additional conditions expressed in Eq. (16) follow immediately from Eqs. (13-15). The conditions given by Eqs. (13-16) describe the essential behavior of the full β function for an effective QCD coupling whose scheme/definition is similar to that of the V scheme. As noted by Grunberg, one can use observables such as heavy quark scattering or the Bjorken sum rule to define effective charges α O ( Q $^{2}$) each with its own physical scale. [9] This generalizes the convention in QED where the Gell Mann-Low coupling [47] α$_{QED}$ ( Q $^{2}$) VI. EFFECTIVE CHARGES AND COMMENSURATE SCALE RELATIONS 14