  The combination of Anti-de Sitter space (AdS) methods with light-front (LF)
holography provides a remarkably accurate first approximation for the spectra
and wavefunctions of meson and baryon light-quark bound states. The resulting
bound-state Hamiltonian equation of motion in QCD leads to relativistic
light-front wave equations in terms of an invariant impact variable $\zeta$
which measures the separation of the quark and gluonic constituents within the
hadron at equal light-front time. These equations of motion in physical
space-time are equivalent to the equations of motion which describe the
propagation of spin-$J$ modes in anti--de Sitter (AdS) space. The eigenvalues
give the hadronic spectrum, and the eigenmodes represent the probability
distributions of the hadronic constituents at a given scale. A positive-sign
confining dilaton background modifying AdS space gives a very good account of
meson and baryon spectroscopy and form factors. The light-front holographic
mapping of this model also leads to a non-perturbative effective coupling
$\alpha_s^{AdS}(Q^2)$ which agrees with the effective charge defined by the
Bjorken sum rule and lattice simulations. It displays a transition from
perturbative to nonperturbative conformal regimes at a momentum scale $ \sim 1$
GeV. The resulting $\beta$-function appears to capture the essential
characteristics of the full $\beta$-function of QCD, thus giving further
support to the application of the gauge/gravity duality to the confining
dynamics of strongly coupled QCD.
