Hadronic Spectrum of a Holographic Dual of QCD

Core claim

The authors propose that the light hadron spectrum is the spectrum of string modes propagating in a slice of $AdS_5 × S^5$ ending at a hard wall at $z_0 = 1/Î}QCD$, with each mode's bulk mass fixed by matching its short-distance scaling to the dimension of the boundary interpolating operator for that hadron's valence Fock state. Solving the resulting wave equations with Dirichlet conditions at the wall gives $M_{α,k} = β_{α,k}Î}QCD$, where $β_{α,k}$ is the $k$-th zero of a Bessel function and $α = 1+L$ for vector mesons ($Δ = 3+L$) and $α = 2+L$ for glueballs ($Δ = 4+L$) and for baryons ($Δ = 9/2+L$). A single scale fits the light meson orbital states at $Î}QCD = 0.263$ GeV and the nucleon and $Δ$ orbital states at $0.22$ GeV. The parameter-free prediction the authors single out is the ratio of the $Δ$ to nucleon trajectories, which is a ratio of Bessel zeros. For baryons the Dirac equation on the slice yields two towers, $M^+_{α,k} = β_{α,k}Î}QCD$ and $M^-_{α,k} = β_{α+1,k}Î}QCD$, so states of opposite parity in neighboring trajectories are predicted to be degenerate, as the observed $N(1650)$, $N(1675)$, $N(1700)$ versus $N(1680)$, $N(1720)$ and the $Δ(1905)$–$Δ(1950)$ cluster versus $Δ(1930)$ appear to be. The lightest glueball $Θ^{++}$ comes out near $1.3$ GeV for $Î}QCD = 0.26$ GeV, and the lowest modes are exactly the two-gluon, three-quark and quark-antiquark color singlets, with no exotic combinations at leading order.