  The combination of Anti-de Sitter space (AdS) methods with light-front
holography leads to a semi-classical first approximation to the spectrum and
wavefunctions of meson and baryon light-quark bound states. 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 distributions of the
hadronic constituents at a given scale. Applications to the light meson and
baryon spectra are presented. The predicted meson spectrum has a string-theory
Regge form ${\cal M}^2 = 4 \kappa^2(n+L+S/2)$; i.e., the square of the
eigenmass is linear in both L and n, where n counts the number of nodes of the
wavefunction in the radial variable zeta. The space-like pion and nucleon form
factors are also well reproduced. One thus obtains a remarkable connection
between the description of hadronic modes in AdS space and the Hamiltonian
formulation of QCD in physical space-time quantized on the light-front at fixed
light-front time. The model can be systematically improved by using its
complete orthonormal solutions to diagonalize the full QCD light-front
Hamiltonian or by applying the Lippmann-Schwinger method in order to
systematically include the QCD interaction terms.
