On the Ubiquity of (Almost) Contact Structures in Hot MQCD at Intermediate Coupling

Relevant to top-down ${\cal M}$-theory dual of large-$N$ thermal QCD-like theories at intermediate coupling, induced by the $G_2$ structure supported by the closed $M_7$ - a warped product of the ${\cal M}$-theory circle and a non-K\"{a}hler six-fold which is the warped product of the thermal circle with a non-Einsteinian deformation of $T^{1,1}$ - we obtain explicitly (Almost) Contact (3) (Metric)Structure(s) and a three-tuple of $SU(3)$ structures along the "transverse" six-fold induced by the AC(3)MS on $M_7$. A novel result in this context is that in the Infra-Red, within the parameter space of AC3S arising from G2 structures, the subspaces of C3S and AC3S are not mutually "N-path connected". Relevance of the results to staying out of the non-supersymmetric swampland, entanglement entropy of eternal black holes, chaos, bulk-to-shear viscosity ratio $\frac{\zeta}{\eta}$, paramagnetic plasma EoS and photoproduction in a strong magnetic field, in the context of top-down holographic thermal QCD at intermediate coupling, is highlighted/reiterated.