On $M$-theory dual of large-$N$ thermal QCD-like theories up to $\mathcal{O}(R^4)$ and $G$-structure classification of underlying non-supersymmetric geometries

Construction of a top-down holographic dual of thermal QCD-like theories (equivalence class of theories which are UV-conformal, IR-confining and have fundamental quarks) at intermediate ’t Hooft coupling and the $G$-structure (torsion classes) classification of the underlying geometries (in the Infra Red (IR)/non-conformal sector in particular) of the non-supersymmetric string/$\mathcal{M}$-theory duals, have been missing in the literature. We take the first important steps in this direction by studying the $\mathcal{M}$ theory dual of large-$N$ thermal QCD-like theories at intermediate gauge and ’t Hooft couplings and obtaining the $\mathcal{O}(l^6_p)$ corrections arising from the $\mathcal{O}(R^4)$ terms to the “MQGP” background ($\mathcal{M}$-theory dual of large-$N$ thermal QCD-like theories at intermediate gauge/string coupling, but large ’t Hooft coupling) of$\href{https://doi.org/10.1007/JHEP11(2013)001}{[1]}$. The main Physics lesson learnt is that there is a competition between non-conformal IR enhancement and Planckian and large-$N$ suppression and going to orders beyond the $\mathcal{O}(l^6_p)$ is necessitated if the IR enhancement wins out. The main lesson learnt in Math is in the context of the differential geometry ($G$-structure classification) of the internal manifolds relevant to the string/$\mathcal{M}$-theory duals of large-$N$ thermal QCD-like theories, wherein we obtain for the first time inclusive of the$\mathcal{O}(R^4)$ corrections in the Infra-Red (IR), the $SU(3)$-structure torsion classes of the type IIA mirror of $\href{https://doi.org/10.1016/j.nuclphysb.2010.06.014}{[2]}$ (making contact en route with Siegel theta functions related to appropriate hyperelliptic curves, as well as the Kiepert’s algorithm of solving quintics), and the $G_2 / SU(4)/Spin(7)$-structure torsion classes of the seven-and eight-folds associated with its $\mathcal{M}$ theory uplift.

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Published 25 March 2024