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
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| Formato: | Preprint |
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2020
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| _version_ | 1866910405500076032 |
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| author | Yadav, Vikas Misra, Aalok |
| author_facet | Yadav, Vikas Misra, Aalok |
| contents | 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/${\cal M}$-theory duals, have been missing in the literature. We take the first important steps in this direction by studying the ${\cal M}$ theory dual of large-$N$ thermal QCD-like theories at intermediate gauge and 't Hooft couplings and obtaining the ${\cal O}(l_p^6)$ corrections arising from the ${\cal O}(R^4)$ terms to the "MQGP" background (${\cal M}$-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 ${\cal O}(l_p^6)$ 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/${\cal M}$-theory duals of large-$N$ thermal QCD-like theories, wherein we obtain for the first time inclusive of the ${\cal O}(R^4)$ corrections in the Infra-Red (IR), the $SU(3)$-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 $G_2/SU(4)/Spin(7)$-structure torsion classes of the seven- and eight-folds associated with its ${\cal M}$ theory uplift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_07259 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | 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 Yadav, Vikas Misra, Aalok High Energy Physics - Theory Differential Geometry 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/${\cal M}$-theory duals, have been missing in the literature. We take the first important steps in this direction by studying the ${\cal M}$ theory dual of large-$N$ thermal QCD-like theories at intermediate gauge and 't Hooft couplings and obtaining the ${\cal O}(l_p^6)$ corrections arising from the ${\cal O}(R^4)$ terms to the "MQGP" background (${\cal M}$-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 ${\cal O}(l_p^6)$ 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/${\cal M}$-theory duals of large-$N$ thermal QCD-like theories, wherein we obtain for the first time inclusive of the ${\cal O}(R^4)$ corrections in the Infra-Red (IR), the $SU(3)$-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 $G_2/SU(4)/Spin(7)$-structure torsion classes of the seven- and eight-folds associated with its ${\cal M}$ theory uplift. |
| title | 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 |
| topic | High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2004.07259 |