String/${\cal M}$-theory Dual of Large-$N$ Thermal QCD-Like Theories at Intermediate Gauge/'t Hooft Coupling and Holographic Phenomenology

Abstract: Considering the setup of arXiv:0902.1540 [hep-th] involving UV-complete top-down type IIB holographic dual of large-N thermal QCD with a fluxed resolved warped deformed conifold, in arXiv:1306.4339 [hep-th] delocalized type IIA S(trominger)-Y(au)-Z(aslow)mirror of the type IIB background of arXiv:0902.1540 [hep-th] was constructed via three T dualities along a special Lagrangian $T^{3}$ fibered over a large base and then uplifted, locally, to the 11-dimensional ${\cal M}$-theory. Considering the aforementioned setup arXiv:1306.4339 [hep-th] in the MQGP' limit, in arXiv:1703.01306 [hep-th] we obtained the masses of the $0^{++}, 0^{-+},0^{--}, 1^{++}, 2^{++}$ (glueball') states. We also obtained analytical expressions for the vector and scalar meson spectra in arXiv:1707.02818 [hep-th]. We used WKB quantization conditions and Neumann/Dirichlet boundary conditions at an IR cut-off ($r_0$')/horizon radius ($r_h$') on the solutions to the equations of motion. We also discussed the $r_h=0$-limits of all calculations which correspond to the thermal background. Subsequently, in arXiv:1808.01182 [hep-th] we obtained the interaction Lagrangian corresponding to exotic scalar glueball $\left( G_{E}\right)-\rho/\pi$- meson. Assuming $M_G>2M_\rho$, we then computed $\rho\rightarrow2\pi, G_E\rightarrow2\pi, 2\rho, \rho+2\pi$ decay widths as well as the direct and indirect (mediated via $\rho$ mesons) $G_E\rightarrow4\pi$ decays. In arXiv:2004.07259 [hep-th] we obtained ${\cal O}\left(l_p^6\right)$ corrections to the MQGP background of arXiv:1306.4339 [hep-th] to study a top-down holographic dual of the thermal QCD-like theories at intermediate 't Hooft coupling and in arXiv:2011.04660 [hep-th] we obtained the values of the coupling constants of the ${\cal O}(p^4)$ $\chi$PT Lagrangian in the chiral limit, inclusive of the ${\cal O}(R^4)$ corrections.