Application of top-down holographic thermal QCD at finite coupling

Abstract

Using the UV-complete top-down type IIB holographic dual of large-$N$ thermal QCD as constructed in arXiv:hep-th/0902.1540, in arXiv:1507.02692[hep-th], the type IIB background of arXiv:hep-th/0902.1540 was shown to be thermodynamically stable. We also showed that the temperature dependence of DC electrical conductivity mimics a one-dimensional Luttinger liquid, and the requirement of the Einstein relation to be satisfied requires a specific dependence of the Ouyang embedding parameter on the horizon radius. In arXiv:1606.04949[hep-th], we obtained the speed of sound, the shear mode diffusion constant and the shear viscosity $η$ (and $\fracη{s}$) upto (N)ext to (L)eading (O)rder in $N$ by looking at the scalar, vector and tensor modes of metric perturbations and solve Einstein's equation involving appropriate gauge-invariant combination of perturbations as constructed in arXiv:hep-th/0506184. Another interesting result for the temperature dependence of the thermal (and electrical) conductivity and the consequent deviation from the Wiedemann-Franz law, upon comparison with arXiv:0903.3054[cond-mat], was obtained at leading order in $N$. The results for the above qualitatively mimic a 1+1-dimensional Luttinger liquid with impurities. Also we obtained the QCD deconfinement temperature compatible with lattice results. On the holographic phenomenology side, in arXiv:1703.01306 [hep-th], we computed the masses of the $0^{++}, 0^{-+},0^{--}, 1^{++}, 2^{++}$ `glueball' states in the same aforementioned backgrounds. All these calculations were done both for a thermal background with an IR cut-off $r_0$ and a black hole background with horizon radius $r_h$. We used WKB quantization conditions on one hand and imposed Neumann/Dirichlet boundary conditions at $r_0$/$r_h$ on the solutions to the equations of motion on the other.