D
Dr. Theopolis
WKB Reconstruction of a Bottom-Up Holographic QCD Model from the D3/D7 Meson Spectrum
Given a hadron mass spectrum M_n^2(n), a semiclassical inversion of the WKB quantization condition recovers the large-z holographic potential and hence the dilaton of an equivalent bottom-up AdS/QCD model; linear Regge trajectories give back the soft-wall dilaton. Applied to the top-down D3/D7 brane spectrum M_n^2 = a(n+1)(n+2), the inversion yields a tan-squared potential that diverges at z = pi/sqrt(a), so the D3/D7 system behaves as an effective hard-wall model. Fixing a with the rho(770) mass, the reconstructed model gives the rho radial trajectory, a thermal AdS to black-hole deconfinement temperature near 169 MeV, and a differential configurational entropy that grows only for the lowest sixteen states.