Regge Trajectories for Mesons in the Holographic Dual of Large-N_c QCD

TL;DR

This work develops a holographic description of meson Regge trajectories in large-$N_c$ QCD by embedding flavor D6 branes in a near-extremal D4-brane background and modeling mesons as rotating open strings with massive endpoints. It derives explicit energy-angular momentum relations, e.g. $E=\frac{2T_g}{\omega}\left(\arcsin x + \frac{1}{x}\sqrt{1-x^2}\right)$ and $J=\frac{T_g}{\omega^2}\left(\arcsin x + \frac{3}{2} x\sqrt{1-x^2}\right)$ with $x=\omega R_0$, showing that massless endpoints yield linear Regge behavior while finite quark masses produce nonlinear corrections consistent with lattice QCD. A sewing condition ties the endpoint mass to the radial position and, at high spin, yields a universal slope $J\sim E^2/(\pi T_g)$. The results provide a microscopic string-theoretic foundation for the mass-loaded Chew-Frautschi phenomenology and capture the qualitative features of heavy- and light-quark meson trajectories observed in lattice studies.

Abstract

We discuss Regge trajectories of dynamical mesons in large-N_c QCD, using the supergravity background describing N_c D4-branes compactified on a thermal circle. The flavor degrees of freedom arise from the addition of N_f<<N_c D6 probe branes. Our work provides a string theoretical derivation, via the gauge/string correspondence, of a phenomenological model describing the meson as rotating point-like massive particles connected by a flux string. The massive endpoints induce nonlinearities for the Regge trajectory. For light quarks the Regge trajectories of mesons are essentially linear. For massive quarks our trajectories qualitatively capture the nonlinearity detected in lattice calculations.

Figures (4)

• Figure 1: The toy model.
• Figure 2: String ending on the probe D6.
• Figure 3: The bottomonium trajectory bottomdatabottom.
• Figure 4: A parametric plot of (\ref{['trajectory']}) for $x\to1$ shows similarity with the bottomonium trajectory.