Contact SHIV SoS or Contact Structure Holographique at Intermediate coupling and bulk Viscosity, and Speed of Sound

Thermal QCD systems like strongly coupled QGP require not only a large 't-Hooft coupling but also a finite gauge coupling arXiv:hep-ph/0701201. Unlike almost all top-down holographic models in the literature, holographic large-N thermal QCD models based on this assumption, therefore necessarily require addressing this limit from M theory. In the context of strongly coupled (very large `t-Hooft coupling), bulk viscosity ζ of the type IIA-theory dual of thermal QCD-like theories was found to vary like 1/3 - cₛ² arXiv:1807.04713 (cₛ being the speed of sound), and the same at weak coupling using kinetic theory and finite temperature field theory, was shown in arXiv:1807.04713 to vary like (1/3 - cₛ²)². In this paper, we not only show that at intermediate coupling, ζ varies like a linear combination of the strong and weak coupling results, but also observe that this behavior is related to the existence of Contact 3-Structures that exists only at intermediate coupling effected by the intermediate-N "MQGP" limit arXiv:2211.13186.