  One of the most fundamental problems in Quantum Chromodynamics is to
understand the origin of the mass scale which controls the range of color
confinement and the hadronic spectrum. We show that a mass gap and a
fundamental color confinement scale arise when one extends the formalism of de
Alfaro, Fubini and Furlan to frame-independent light-front Hamiltonian theory.
Remarkably, the resulting light-front potential has a unique form of a harmonic
oscillator in the light-front invariant impact variable if one requires that
the action remains conformally invariant. The result is a single-variable
relativistic equation of motion for $q \bar q$ bound states, a "Light-Front
Shr\"odinger Equation", analogous to the nonrelativistic radial Schr\"odinger
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 with the same slope in
the radial quantum number and orbital angular momentum. The same equations with
the correct hadron spin dependence arise from the holographic mapping of
modified AdS$_5$ space with a specific dilaton profile. A fundamental mass
parameter $\kappa$ appears, determining the hadron masses and the length scale
which underlies hadron structure. Quark masses can be introduced to account for
the spectrum of strange hadrons. This Light-Front Holographic approach predicts
not only hadron spectroscopy successfully, but also hadronic form factors, the
QCD running coupling at small virtuality, and the light-front wavefunctions of
hadrons. Thus the combination of light-front dynamics, its holographic mapping
to gravity in a higher-dimensional space and the dAFF procedure provides new
insight into the physics underlying color confinement, chiral invariance, and
the QCD mass scale.

High Energy Physics - Theory;High Energy Physics - Phenomenology