Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra and other Advances in Light-Front QCD

Abstract

Light-front holography, together with superconformal algebra, have provided new insights into the physics of color confinement and the spectroscopy and dynamics of hadrons. As shown by de Alfaro, Fubini and Furlan, 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 procedure of de Alfaro et al. to the frame-independent light-front Hamiltonian, it leads uniquely to a confining $q \bar{q}$ potential $\kappa ^4 \zeta ^2$, where $\zeta ^2$ is the light-front radial variable related in momentum space to the $q \bar{q}$ invariant mass. The same result, including spin terms, is obtained using light-front holography—the duality between the front form and AdS$_5$, the space of isometries of the conformal group—if one modifies the action of AdS$_5$ 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 lead to a a unified Regge spectroscopy of meson, baryon, and tetraquarks, including supersymmetric relations between their masses and their wavefunctions. One also predicts hadronic light-front wavefunctions and observables such as structure functions, transverse momentum distributions, and the distribution amplitudes. The mass scale $\kappa$ underlying confinement and hadron masses can be connected to the parameter $\varLambda _{\overline{MS}}$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling $\alpha _s(Q^2)$ defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale $Q_0$ which sets the interface between perturbative and nonperturbative hadron dynamics. I also discuss a number of applications of light-front phenomenology.