  We find a correspondence between semiclassical QCD quantized on the
light-front and a dual gravity model in anti--de Sitter (AdS) space, thus
providing an initial approximation to QCD in its strongly coupled regime. This
correspondence -- light-front holography -- leads to a light-front Hamiltonian
and relativistic bound-state wave equations that are functions of an invariant
impact variable $\zeta$ which measures the separation of the quark and gluonic
constituents within hadrons at equal light-front time. The eigenvalues of the
resulting light-front Schr\"odinger and Dirac equations are consistent with the
observed light meson and baryon spectrum, and the eigenmodes provide the
light-front wavefunctions, the probability amplitudes describing the dynamics
of the hadronic constituents. The light-front equations of motion, which are
dual to an effective classical gravity theory, possess remarkable algebraic and
integrability properties which are dictated by the underlying conformal
properties of the theory. We extend the algebraic construction to include a
confining potential while preserving the integrability of the mesonic and
baryonic bound-state equations.
