Top-Down Holographic $G$-Structure Glueball Spectroscopy at (N)LO in $N$ and Finite Gauge Coupling

Abstract

The top-down type IIB holographic dual of large-$N$ thermal QCD as constructed in arXiv:0902.1540 involving a fluxed resolved warped deformed conifold, its delocalized type IIA SYZ mirror as well as its M-theory uplift constructed in arXiv:1306.4339 - both in the finite gauge coupling ($g_s\stackrel{<}{\sim }1$)/`MQGP' limit of arXiv:1306.4339 - were shown explicitly to possess a local $SU(3)/G_2$-structure in arXiv:1507.02692 Glueball spectroscopy at finite gauge coupling 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 arXiv:1306.4339, using WKB quantization conditions on one hand and imposing Neumann/Dirichlet boundary conditions at an IR cut-off/horizon radius $r_h$ on the solutions to the equations of motion on the other. We also discuss $r_h=0$-limits of all calculations; in this context we also calculate the $0^{++},0^{--},1^{++},2^{++}$ glueball masses up to NLO in $N$ and find a $\frac{g_s{M}^2}{N}(g_s{N}_f)$-suppression similar to and further validating a similar semi-universality of NLO corrections to transport coefficients, observed in arXiv:1606.04949.

v2:1+55 pages, LaTeX; references and clarifying remarks added, shortened by deleting old appendices, a sub-section and a table; to appear in Eur.Phys.J.C

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