system, m$_{red}$ = m$_{Q}$m$_{Q}$/ ( m$_{Q}$ + m$_{Q}$ ), and ω = κ $^{2}$/ ( m$_{Q}$ + m$_{Q}$ ). Remarkably, the explicit holographic confining potential V$_{conf}$ , which is the dominant interaction for light quarks, vanishes as the inverse of the quark mass for heavy quark masses. 

For finite quark masses both contributions will appear. This will bring the effective potential closer to the phenomenological Cornell potential. Thus, the comparison of the Coulomb results in Fig. 6 with the Cornell potential only holds in the limit of infinite quark masses. A detailed discussion of the confining interaction, its implication for the study of the heavy meson mass spectrum, and other aspects of the instantaneous quark-antiquark potential will be discussed elsewhere. 

## IX. CONCLUSIONS 

We have shown that the light-front holographic mapping of effective classical gravity in AdS space, modified by a positive-sign dilaton background exp (+ κ $^{2}$z$^{2}$), can be used to identify a nonperturbative effective coupling α AdS s ( Q ) and its β function. The same theory provides a very good description of the spectrum and form factors of light hadrons. Our analytical results for the effective holographic coupling provide new insights into the infrared dynamics and the form of the full β function of QCD. 

We also observe that the effective charge obtained from light-front holography is in very good agreement with the effective coupling α$_{g}$$_{1}$ extracted from the Bjorken sum rule. Sur- prisingly, the Furui and Nakajima lattice results [38] also agree better overall with the g$_{1}$ scheme rather than the V scheme as seen in Fig. 5. Our analysis indicates that light-front holography captures the essential dynamics of confinement, showing that it belongs to a uni- versality class of models with built-in confinement. The holographic β function shows the transition from nonperturbative to perturbative regimes at a momentum scale Q ∼ 1 GeV and captures some of the essential characteristics of the full β function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. 

We have made extensive use of commensurate scale relations, which allows us to relate observables in different schemes and regimes. In particular, we have extrapolated the CSR to extend the relation between observables to the nonperturbative domain. In the pQCD domain, we checked that the CSR are valid. This validity provides a fundamental check of 

