by 1 /N$_{C}$ . We can identify the prefactor in the AdS action (5) as the effective coupling of the theory at the length scale z . The coupling g$_{5}$ ( z ) then incorporates the nonconformal dynamics of confinement. The five- dimensional coupling g$_{5}$ ( z ) is mapped, modulo a constant, into the Yang-Mills (YM) cou- pling g$_{YM}$ of the confining theory in physical space-time using light-front holography. One identifies z with the invariant impact separation variable ζ which appears in the LF Hamil- tonian: g$_{5}$ ( z ) → g$_{YM}$ ( ζ ). Thus In contrast with the three-dimensional radial coordinates of the nonrelativistic Schr¨ odinger theory, the natural light-front variables are the two-dimensional cylindrical coordinates ( ζ, φ ) and the light-cone fraction x . The physical coupling measured at the scale Q is the two- dimensional Fourier transform of the LF transverse coupling α AdS s ( ζ ) (7). Integration over the azimuthal angle φ gives the Bessel transform in the q + = 0 light-front frame where Q 2 = − q 2 = − q 2 ⊥ > 0 is the square of the spacelike four-momentum transferred to the hadronic bound state. Using this ansatz we then have from Eq. (8) In contrast, the negative dilaton solution ϕ = − κ $^{2}$z2 leads to an integral that diverges at large ζ . The essential assumption of this paper is the identification of α AdS s ( Q $^{2}$) with the physical QCD running coupling in its nonperturbative domain. The flow Eq. (6) from the scale-dependent measure for the gauge fields can be under- stood as a consequence of field-strength renormalization. In physical QCD we can rescale the non-Abelian gluon field A µ → λA µ and field strength G µν → λG µν in the QCD Lagrangian density L QCD by a compensating rescaling of the coupling strength g → λ − $^{1}$g. The renor- malization of the coupling g$_{phys}$ = Z 1 / 2 3 g$_{0}$, where g$_{0}$ is the bare coupling in the Lagrangian in the UV-regulated theory, is thus equivalent to the renormalization of the vector potential and field strength: A µ ren = Z − 1 / 2 3 A µ $_{0}$, G µν ren = Z − 1 / 2 3 G µν 0 with a rescaled Lagrangian density α AdS s ( Q $^{2}$) ∼ ∫ ∞ 0 ζdζ J$_{0}$ ( ζQ ) α AdS s ( ζ ) , (8) α AdS s ( ζ ) = g 2 $_{YM}$( ζ ) / 4 π ∝ e − κ $^{2}$ζ$^{2}$. (7) g − 2 5 ( z ) = e ϕ ( z $^{)}$g − 2 5 , (6) 9 α AdS s ( Q $^{2}$) = α AdS s (0) e − Q $^{2}$/ 4 κ $^{2}$. (9)