Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x + = x 0 + x 3 , provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian HLF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schr¨odinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of HLF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable ζ 2 = b 2 ⊥x(1−x), which is conjugate to the invariant mass squared M2 qq¯. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories M2 (n, L, S) = 4κ 2 (n+L+S/2) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant
