Baryon spectrum from superconformal quantum mechanics and its light-front holographic embedding

We describe the observed light-baryon spectrum by extending superconformal quantum mechanics to the light front and its embedding in AdS space. This procedure uniquely determines the confinement potential for arbitrary half-integer spin. To this end, we show that fermionic wave equations in AdS space are dual to light-front supersymmetric quantum-mechanical bound-state equations in physical space-time. The specific breaking of conformal invariance explains hadronic properties common to light mesons and baryons, such as the observed mass pattern in the radial and orbital excitations, from the spectrum generating algebra. The holographic embedding in AdS also explains distinctive and systematic features, such as the spin-$J$ degeneracy for states with the same orbital angular momentum, observed in the light-baryon spectrum.

Figure 1

Orbital and radial baryon excitation spectrum. (a) Positive-parity spin-$\frac{1}{2}$ nucleons and (b) spectrum gap between the negative-parity spin-$\frac{3}{2}$ and the positive-parity spin-$\frac{1}{2}$ nucleons families. (c) Minus-parity spin-$\frac{1}{2}$ $N$ and (d) plus- and minus-parity spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ $\mathrm{\Delta }$ families. We have used in this figure the value $\sqrt{{\lambda }_B}=0.49\mathrm{GeV}$ for nucleons and 0.51 GeV for the deltas.