Light-Front Holography and Gauge/Gravity Duality: The Light Meson and Baryon Spectra

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.