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

Abstract

The combined approach of light-front holography and superconformal algebra provides insight into the origin of color confinement and the QCD mass scale. Light-front (LF) holography predicts Lorentz-invariant light-front Schr\"odinger bound state equations for QCD, analogous to the quantum mechanical Schrodinger equation for atoms in QED. A key feature is the implementation of the de Alfaro, Fubini and Furlan (dAFF) procedure for breaking conformal invariance which allows a mass parameter to 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 hadron masses and universal Regge slopes. It also implies a unique form of the soft-wall dilaton which modifies the action of AdS$_5$. The result is a remarkably simple analytic description of quark confinement, as well as nonperturbative hadronic structure and dynamics. The same mass parameter $\kappa$ controls the Gaussian fall-off of the nonperturbative QCD running coupling: $\alpha_s(Q^2) \propto \exp{\left(-Q^2/4 \kappa^2\right)}$, in agreement with the effective charge determined from measurements of the Bjorken sum rule. The mass scale $\kappa$ underlying hadron masses can be connected to the parameter $\Lambda_{\overline {MS}}$ in the QCD running coupling by matching the magnitude and slope of the nonperturbative coupling to perturbative QCD at large $Q^2$. The result is an effective coupling $\alpha_s(Q^2)$ defined at all momenta and a transition scale $Q_0$ which separates perturbative and nonperturbative dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, when one applies superconformal algebra, one obtains a unified spectroscopy of meson, baryon, and tetraquarks as equal-mass members of the same 4-plet representation. The LF resulting Schrodinger equations match the bound state equation obtained from LF holography. The predicted Regge trajectories have a universal slope in both the principal quantum number $n$ and orbital angular momentum. The meson and baryon Regge trajectories are identical when one compares mesons with baryons with orbital angular momentum $L_M= L_B +1$. The matching of bosonic meson and fermionic baryon masses is a manifestation of a hidden supersymmetry in hadron physics. The pion eigenstate is massless for massless quarks, despite its dynamical structure as a $q \bar q$ bound state. The superconformal relations also can be extended to heavy-light quark mesons and baryons. One also obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.