  Starting from the bound state Hamiltonian equation of motion in QCD, we
derive 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. Its
eigenvalues give the hadronic spectrum, and its eigenmodes represent the
probability amplitudes of the hadronic constituents at a given scale. An
effective classical gravity description in a positive-sign dilaton background
$\exp(+ \kappa^2 z^2)$ is given for the phenomenologically successful soft-wall
model which naturally encodes the internal structure of hadrons and their
orbital angular momentum. Applications to the light meson and baryon spectrum
are presented.
