Tc$T_c$, Photoproduction, Paramagnetic Anisotropic Plasma, IR Log‐Gravitational‐DBI Renormalization, and G2$G_2$‐Structure Induced (Almost) Contact 3‐Structures in Hot Strongly Magnetic MQCD at Intermediate Coupling

Abstract After obtaining the gauge fields that can be supported on the world‐volume of flavor ‐branes in the type IIA dual of thermal QCD‐like theories at high temperatures and intermediate coupling (the latter incorporated via the inclusion of corrections in its ‐theory uplift), combining with the results of Yadav et al., it is shown that the deconfinement temperature decreases in the presence of a strong magnetic field as in lattice QCD. By working out gauge‐invariant fluctuations about the aforementioned world‐volume gauge fields, in the (absence and) presence of a strong magnetic field ( in ‐units), we obtain the variation ( being the spectral function for the in(reaction)‐plane photon polarization and being the number of color ‐branes in the parent type IIB dual of thermal QCD‐like theories). We further obtain a nice agreement with, e.g., bottom‐up holographic anisotropic backgrounds in gauged supergravity. Implementing Dirichlet boundary condition at the horizon for the world‐volume gauge fields, we also demonstrate at the level of EoS that the holographic dual, in principle, could correspond to several scenarios above . These include (i) the anisotropic plasma transitioning via a smooth crossover to exotic matter as the universe cools (the converse being prohibited in our setup), (ii) stable wormholes (where we also remark that a resolved conifold near is somewhat like a half Ellis wormhole), and (iii) a paramagnetic pressure/energy‐anisotropic plasma. Given that above QGP is expected to be paramagnetic, the third possibility appears to be the preferred one. Generalizing the TOV equations to include angular mass/pressure/energy profiles, we show up to first order in , that it is not possible that the anisotropic plasma leads to the formation of a compact star. En route, we show that the IR renormalization of the DBI action requires a boundary Log‐determinant‐of‐Ricci‐tensor counter term. We further conjecture that (i) quantities like photoproduction spectral function, speed of sound (and hence bulk viscosity), etc., in the absence of a magnetic field that are determined from world‐volume gauge field fluctuations that receive ‐corrections, if complexified, include a non‐analytic‐complexified gauge‐coupling dependence, and correspond to Contact 3‐Structures; (ii) quantities, e.g., pressure/free energy, energy density, etc. in the presence of a strong magnetic field that are determined from world‐volume gauge fields that are not ‐corrected, if complexified, are analytic in the complexified gauge coupling, and correspond to Almost Contact 3‐Structures (AC3S), both induced from the structure of a closed seven‐fold—a warped product of the ‐theory circle and a non‐Kähler six‐fold with the six‐fold being a warped product of the thermal circle with a non‐Einsteinian deformation of , and (iii) the lack of ‐path connectedness in the parameter space associated with AC3S and C3S, corresponds therefore to that gauge field fluctuations can not be finite, and in the zero‐instanton sector, (type‐IIB modular‐completion‐inspired) non‐renormalized gauge fields produce ‐corrected gauge fluctuations.