Top-down holographic G-structure glueball spectroscopy at (N)LO in N and finite coupling

The top-down type IIB holographic dual of large-N thermal QCD as constructed in Mia et al. (Nucl Phys B 839:187, 2010) involving a fluxed resolved warped deformed conifold, its delocalized type IIA Strominger-Yau-Zaslow-mirror (SYZ-mirror) as well as its M-theory uplift constructed in Dhuria and Misra (JHEP 1311:001, 2013) - both in the finite coupling g_s 2-structure in Sil and Misra (Nucl Phys B 910:754, 2016). Glueballs spectra in the finite-gauge-coupling limit (and not just large 't Hooft coupling limit) - a limit expected to be directly relevant to strongly coupled systems at finite temperature such as QGP (Natsuume in String theory and quark-gluon plasma, 2007) - has thus far been missing in the literature. In this paper, we fill this gap by calculating the masses of the 0⁺⁺, 0^-+, 0^--, 1⁺⁺, 2⁺⁺ ('glueball') states (which correspond to fluctuations in the dilaton or complexified two-forms or appropriate metric components) in the aforementioned backgrounds of G-structure in the 'MQGP' limit of Dhuria and Misra (JHEP 1311:001, 2013). We use WKB quantization conditions on one hand and impose Neumann/Dirichlet boundary conditions at an IR cut-off ('r₀')/horizon radius ('r_h') on the solutions to the equations of motion on the other hand. We find that the former technique produces results closer to the lattice results. We also discuss the r_h = 0 limits of all calculations. In this context we also calculate the 0⁺⁺, 0^--, 1⁺⁺, 2⁺⁺ glueball masses up to Next to Leading Order (NLO) in N and find a (g_sM²)/(N)(g_sN_f)-suppression similar to and further validating semi-universality of NLO corrections to transport coefficients, observed in Sil and Misra (Eur Phys J C 76(11):618, 2016). (orig.)