Bulk viscosity, speed of sound, and contact structure at intermediate coupling

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Thermal QCD systems like strongly coupled quark gluon plasma require not only a large ’t Hooft coupling but also a finite gauge coupling [Natsuume, ] in the large-N gravity dual. 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) thermal QCD-like theories, the bulk-viscosity(ζ)-to-shear-viscosity(η) ratio using the type-IIA-theory dual of thermal QCD-like theories was shown to vary like 13−cs2 [Czajka , Bulk viscosity at extreme limits: From kinetic theory to strings, ] (cs being the speed of sound), and the same (ζη) at weak coupling using kinetic theory and finite temperature field theory was shown and is known to vary like (13−cs2)2 [Czajka , Bulk viscosity at extreme limits: From kinetic theory to strings, , and references therein]. The novelties of the results of this paper are that we not only show for the first time from M theory that at intermediate coupling, with the inclusion of the O(R4) corrections, the result obtained for ζη interpolates between the strong- and weak-coupling results in a way consistent with lattice computations of SU(3) gluodynamics [Meyer, Calculation of the bulk viscosity in SU(3) gluodynamics, ] within statistical errors (and within the temperature range permissible by our M-theory uplift), but also observe that this behavior is related to the existence of contact 3-structures that exist only at intermediate coupling effected by the intermediate-N “MQGP” limit of Misra and Yadav []. We also obtain an explicit dependence of ζη on (fractional powers of) the temperature-dependent and running gauge coupling (and its temperature derivative) and verify that the weak-coupling result dominates at large temperatures. We further conjecture that the aforementioned fractional-power dependence of ζη on the gauge coupling is related to the lack of “N-connectedness” in the parameter space of contact 3-structures (as shown in ). Published by the American Physical Society 2024