APPLICATIONS OF TOP-DOWN HOLOGRAPHIC THERMAL QCD AT FINITE COUPLING

Abstract

Large-N thermal QCD laboratories like strongly coupled QGP (sQGP) require not only a large t’Hooft coupling but also a finite gauge coupling [1]. 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. Using the UV-complete top-down type IIB holographic dual of large-N thermal QCD as constructed in [2] involving a fluxed resolved warped deformed conifold, its delocalized type IIA S(trominger)-Y(au)-Z(aslow) mirror as well as its M-theory uplift constructed in [3], in [4], the type IIB background of [2] 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 require- ment of the Einstein relation (ratio of electrical conductivity and charge suscepti- bility equal to the diffusion constant) to be satisfied requires a specific dependence of the Ouyang embedding parameter on the horizon radius. Any strongly coupled medium behaves like a fluid with interesting transport properties. In [5], we ad- dressed these properties 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 [6]. Due to finite string coupling, i ii we obtained the speed of sound, the shear mode diffusion constant and the shear viscosity (and s ) upto (N)ext to (L)eading (O)rder in N. The NLO terms in each of the coefficients serve as a the non-conformal corrections to the conformal results. Another interesting result for the temperature dependence of the thermal (and elec- trical) conductivity and the consequent deviation from the Wiedemann-Franz law, upon comparison with [7], 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 (a study that was in fact initiated in [4]). On the holographic phenomenology side, in [8], we computed the masses of the 0++, 0−+, 0−−, 1++, 2++ ‘glueball’ states corresponding to fluctuations in the dilaton or complexified two-forms or appropriate metric components in the same aforemen- tioned backgrounds. All these calculations were done both for a thermal background with an IR cut-off r0 and a black hole background with horizon radius rh. We used WKB quantization conditions on one hand and imposed Neumann/Dirichlet bound- ary conditions at r0/rh on the solutions to the equations of motion on the other. We found that the former technique produces results closer to the lattice results [9], [10]