On ${\cal M}$-Theory Dual of Large-$N$ Thermal QCD-Like Theories up to ${\cal O}(R^4)$ and $G$-Structure Classification of Underlying Non-Supersymmetric Geometries

Vikas Yadav; Aalok Misra

doi:10.4310/ATMP.2022.v26.n10.a11

paper

On $M$ -Theory Dual of Large- $N$ Thermal QCD-Like Theories up to $O (R^{4})$ and $G$ -Structure Classification of Underlying Non-Supersymmetric Geometries

arXiv:2004.07259 · doi:10.4310/ATMP.2022.v26.n10.a11

Abstract

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) {\it 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 {\it non-supersymmetric} string/ $M$ -theory duals, have been missing in the literature. We take the first important steps in this direction by studying the $M$ theory dual of large- $N$ thermal QCD-like theories at intermediate gauge and 't Hooft couplings and obtaining the $O (l_{p}^{6})$ corrections arising from the $O (R^{4})$ terms to the "MQGP" background ( $M$ -theory dual of large- $N$ thermal QCD-like theories at intermediate gauge/string coupling, but large 't Hooft coupling) of \cite{MQGP}. 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 $O (l_{p}^{6})$ 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/ $M$ -theory duals of large- $N$ thermal QCD-like theories, wherein we obtain for the first time inclusive of the $O (R^{4})$ corrections in the Infra-Red (IR), the $S U (3)$ -structure torsion classes of the type IIA mirror of \cite{metrics} (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 $G_{2} / S U (4) / S p in (7)$ -structure torsion classes of the seven- and eight-folds associated with its $M$ theory uplift.

arXiv commentv5: 1+84 pages, LaTeX, Adv.Theor.Math.Phys. 26 (2022) 10, 3801 - 3894, the paper dedicated by AM to the memory of his father

On M-Theory Dual of Large-N Thermal QCD-Like Theories up to O(R4) and G-Structure Classification of Underlying Non-Supersymmetric Geometries

Abstract

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On $M$ -Theory Dual of Large- $N$ Thermal QCD-Like Theories up to $O (R^{4})$ and $G$ -Structure Classification of Underlying Non-Supersymmetric Geometries