I review applications of superconformal algebra. light-front holography, and an extended form of conformal symmetry to hadron spectroscopy and dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields -- not squarks nor gluinos.
However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD.
The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope.
The pion $q \bar q$ eigenstate is composite but yet has zero mass for $m_q=0.$
Light-Front Holography also predicts the form of the nonperturbative QCD running coupling: $\alpha_s(Q^2) \propto \exp{-{Q^2/4 \kappa^2}}$, in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for tests of hadron dynamics such as spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.
The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement.
A key tool is the dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale $\kappa$ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. The result is an extended conformal symmetry which has a conformally invariant action even though an underlying mass scale appears in the Hamiltonian. Although conformal symmetry is strongly broken by the heavy quark mass, the
supersymmetric mechanism, which transforms
mesons to baryons (and
baryons to tetraquarks), still holds and gives remarkable mass degeneracies across the spectrum of light, heavy-light and double-heavy hadrons.