  Meson spectroscopy at finite gauge coupling - whereat any perturbative QCD
computation would break down - and finite number of colors, from a top-down
holographic string model, has thus far been entirely missing in the literature.
This paper fills in this gap. Using the delocalized type IIA SYZ mirror (with
$SU(3)$ structure) of the holographic type IIB dual of large-$N$ thermal QCD of
arXiv:hep-th/0902.1540 as constructed in arXiv:hep-th/1306.4339 at finite
coupling and number of colors ($N_c$ = Number of $D5(\overline{D5}$)-branes
wrapping a vanishing two-cycle in the top-down holographic construct of
arXiv:hep-th/0902.1540 = ${\cal O}(1)$ in the IR in the MQGP limit of
arXiv:hep-th/1306.4339 at the end of a Seiberg duality cascade), we obtain
analytical (not just numerical) expressions for the vector and scalar meson
spectra and compare our results with previous calculations of hep-th/0412141,
arXiv:1409.0559 [hep-th], and obtain a closer match with the Particle Data
Group (PDG) results (Chin. Phys. C, 38, 090001 (2014) and 2015 update). Through
explicit computations, we verify that the vector and scalar meson spectra
obtained by the gravity dual with a black hole for all temperatures (small and
large) are nearly isospectral with the spectra obtained by a thermal gravity
dual valid for only low temperatures; the isospectrality is much closer for
vector mesons than scalar mesons. The black hole gravity dual (with a horizon
radius smaller than the deconfinement scale) also provides the expected
large-$N$ suppressed decrease in vector meson mass with an increase of
temperature.
