Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

Abstract

The QCD light-front Hamitonian equation derived from quantization at fixed LF time provides a causal, frame-independent, method for computing hadron spectroscopy and dynamical observables. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color confining potential $\kappa^4 \zeta^2$ for mesons, where $\zeta^2$ is the LF radial variable conjugate to the $q \bar q$ invariant mass squared. The same result, including spin terms, is obtained using light-front holography if one modifies the AdS$_5$ action by the dilaton $e^{\kappa^2 z^2}$ in the fifth dimension $z$. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion $q \bar q$ eigenstate has zero mass at $m_q=0.$ The superconformal relations also can be extended to heavy-light quark mesons and baryons. AdS/QCD also predicts the analytic form of the nonperturbative running coupling in agreement with the effective charge measured from measurements of the Bjorken sum rule. The mass scale underlying hadron masses can be connected to the mass parameter in the QCD running coupling. The result is an effective coupling $\alpha_s(Q^2)$ defined at all momenta. One also obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.