L ren QCD = Z − 1 3 L 0 QCD = ( g$_{phys}$/g$_{0}$ ) − $^{2}$L $_{0}$. In lattice gauge theory, the lattice spacing a serves as the UV regulator, and the renormalized QCD coupling is determined from the normalization of the gluon field strength as it appears in the gluon propagator. The inverse of the lattice size L sets the mass scale of the resulting running coupling. As in lattice gauge theory, color confinement in AdS/QCD reflects nonpertubative dynamics at large distances. The QCD couplings defined from lattice gauge theory and the soft-wall holographic model are thus similar in concept, and both schemes are expected to have similar properties in the nonperturbative domain, up to a rescaling of their respective momentum scales. The gauge/gravity correspondence has also been used to study the running coupling of the dual field theory. One can modify the dynamics of the dilaton in the AdS space to simulate the QCD β function in the UV domain. [30–36] For example, a β -function ansatz of the boundary field theory is used as input in Refs. [32–36] to modify the AdS metrics assuming the correspondence between the AdS variable z and the energy scale E of the conformal field theory, E ∼ 1 /z , as discussed in Ref. [37]. In our paper, the effective QCD coupling is identified by using the precise mapping from z in AdS space to the transverse impact variable ζ in LF QCD. The effective coupling α $^{AdS}$( Q $^{2}$) (solid line) is compared in Fig. 1 with experimental and lattice data. For this comparison to be meaningful, we have to impose the same normal- ization on the AdS coupling as the g$_{1}$ coupling. This defines α AdS s normalized to the g$_{1}$ scheme A similar value for the normalization constant is derived in Ref. [22] from the AdS/CFT prediction for the current-current correlator. The value of the five-dimensional coupling found in [22] for a SU (2) flavor gauge theory is ( g 2 $_{5}$)$_{SU}$$_{(2)}$ = 12 π $^{2}$R/N$_{C}$ , and thus ( g 2 5 4 $_{π}$)$_{SU}$$_{(2)}$ = π for N$_{C}$ = 3 in units R = 1. The couplings in Fig. 1 agree well in the strong coupling regime up to Q ∼ 1 GeV. The value κ = 0 . 54 GeV has been determined from the vector meson principal Regge trajec- tory. [7] The lattice results shown in Fig. 1 from Ref. [38] have been scaled to match the IV. COMPARISON OF THE HOLOGRAPHIC COUPLING WITH OTHER EF- FECTIVE CHARGES α AdS g 1 ( Q $^{2}$= 0 ) = π. (10) 10