Hadronic Spectrum of a Holographic Dual of QCD

We compute the spectrum of light hadrons in a holographic dual of QCD defined on ${\mathrm{AdS}}_5\times S^5$ which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron’s valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale ${\Lambda }_{\mathrm{QCD}}$, is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio of delta to nucleon trajectories is determined by the ratio of zeros of Bessel functions.

Figure 1

Light meson orbital states for ${\Lambda }_{\mathrm{QCD}}=0.263\mathrm{GeV}$. Results for the vector mesons are shown in (a) and for the pseudoscalar mesons in (b). The dashed line corresponds to the usual linear Regge trajectory and has slope $1.16{\mathrm{GeV}}^2$.

Figure 2

Light baryon orbital spectrum for ${\Lambda }_{\mathrm{QCD}}=0.22\mathrm{GeV}$. Predictions for the nucleons are shown in (a) and for the $\Delta$ trajectories in (b). The lower dashed curves correspond to baryon states dual to spin-$\frac{1}{2}$ modes in the bulk and the upper continuous curve to states dual to spin-$\frac{3}{2}$ modes.