On aspects of holographic thermal QCD at finite coupling

Abstract

In the context of string theoretic dual of thermal QCD-like theories at finite gauge/string coupling of [1] (as part of the ‘MQGP’ limit of [2]), we obtain the QCD deconfinement temperature compatible with lattice results for the right number of light flavors Nf=3, and the correct mass scale of the light (first generation) quarks. The type IIB background of [1] is also shown to be thermodynamically stable. Further, we show that the temperature dependence of DC electrical conductivity mimics a one-dimensional Luttinger liquid, and the requirement of the Einstein relation (ratio of electrical conductivity and charge susceptibility equal to the diffusion constant) to be satisfied requires a specific dependence of the Ouyang embedding parameter on the horizon radius. These results arise due to the non-Kählerity and non-conformality of the type IIB background. On the geometrical side we quantify the former (non-Kählerity) by evaluating the SU(3)/G2-structure torsion classes of the local type IIA mirror/M-theory uplift. Analogous to what was shown for the type IIB background in [5], we first show that the type IIA delocalized SYZ mirror (after fine tuning) can also be approximately supersymmetric. We then work out the G2-structure torsion classes of the local M-theory uplift of the mirror type IIA metric – in the large-N limit at finite coupling, G2 structure approaches G2 holonomy.