Superconformal baryon-meson symmetry and light-front holographic QCD

We construct an effective QCD light-front Hamiltonian for both mesons and baryons in the chiral limit based on the generalized supercharges of a superconformal algebra. The superconformal construction is shown to be equivalent to a semiclassical approximation to light-front QCD and its embedding in anti–de Sitter space. The specific breaking of conformal invariance inside the superconformal algebra uniquely determines the effective confinement potential. The generalized supercharges connect the baryon and meson spectra to each other in a remarkable manner. In particular, the $\pi /b_1$ Regge trajectory is identified as the superpartner of the nucleon trajectory. However, the lowest-lying state on this trajectory, the $\pi$-meson, is massless in the chiral limit and has no supersymmetric partner.

Figure 1

Meson-nucleon superconformal connection. The predicted value of $M^2$ in units of $4\lambda$ for mesons with $S=0$ (red triangles), and baryons with $S=\frac{1}{2}$ (blue squares) is plotted vs the orbital angular momentum $L$. The $\pi$ meson has no baryonic partner. The baryon quantum number assignment is taken from Ref. [13]. Nucleon trajectories with the same $L$ but dierent $J$ are degenerate.

Figure 2

Supersymmetric meson-nucleon partners: Mesons with $S=0$ (red triangles) and baryons with $S=\frac{1}{2}$ (blue squares). The experimental values of $M^2$ are plotted vs $L_M=L_B+1$. The solid line corresponds to $\sqrt{\lambda }=0.53\mathrm{GeV}$. The $\pi$ has no baryonic partner.

Figure 3

Supersymmetric vector meson and $\mathrm{\Delta }$ partners: Mesons with $I=1$ (red triangles) and $I=0$ (red circles) and $\mathrm{\Delta }$ states with $S=\frac{3}{2}$ and $S=\frac{1}{2}$ (blue squares) for plus and minus parity respectively. The experimental values of $M^2$ are plotted vs $L_M=L_B+1$. The solid line corresponds to $\sqrt{\lambda }=0.53\mathrm{GeV}$. The $\rho$ and $\omega$ have no baryonic partner, since it would imply a negative value of $L_B$.

Figure 4

Radial excitations and transformations by elements of the superconformal algebra for a baryon-meson system with a given $f-\frac{1}{2}=L_B\ge 0$.