Abstract
It is believed that large-N thermal QCD laboratories like strongly coupled QGP (sQGP) require not only a large ‘t Hooft coupling but also a finite gauge coupling (Natsuume, String theory and quark–gluon plasma. arXiv:hep-ph/0701201 , 2007). 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. This was initiated in Dhuria and Misra (JHEP 1311:001, 2013) which presented a local M-theory uplift of the string theoretic dual of large-N thermal QCD-like theories at finite gauge/string coupling of Mia et al. (Nucl. Phys. B 839:187, arXiv:0902.1540 [hep-th], 2010) ( $$g_s\mathop {<}\limits ^{\sim }1$$ as part of the ‘MQGP’ limit of Dhuria and Misra in JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013). Understanding and classifying the properties of systems like sQGP from a top–down holographic model, assuming a finite gauge coupling, have been entirely missing in the literature. In this paper we largely address the following two non-trivial issues pertaining to the same. First, up to LO in N (the number of D3-branes), by calculating the temperature dependence of the thermal (and electrical) conductivity and the consequent deviation from the Wiedemann–Franz law, upon comparison with Garg et al. (Phys. Rev. Lett. 103:096402, 2009), we show that, remarkably, the results qualitatively mimic a 1+1-dimensional Luttinger liquid with impurities. Second, by looking at, respectively, the scalar, vector, and tensor modes of metric perturbations and using the prescription of Kovtun and Starinets (Phys. Rev. D 72:086009, arXiv:hep-th/0506184 , 2005) for constructing appropriate gauge-invariant perturbations, we obtain the non-conformal corrections to the conformal results (but at finite $$g_s$$ ), respectively, for the speed of sound, the shear mode diffusion constant, and the shear viscosity $$\eta $$ (and $$\frac{\eta }{s}$$ ). The new insight gained is that it turns out that these corrections show a partial universality in the sense that at NLO in N the same are given by the product of $$\frac{(g_s M^2)}{N}\ll 1$$ and $$g_s N_f\sim \mathcal{O}(1)$$ , $$N_f$$ being the number of flavor D7-branes and M the number of fractional D3-branes = the number of colors = 3 in the IR after the end of a Seiberg-duality cascade. On the mathematics side, using the results of Ionel and Min-OO (Ill. J. Math. 52, 2008), at LO in N we finish our argument of Dhuria and Misra (Eur. Phys. J. C 75:16, 2015) and show that for a predominantly resolved (resolution > deformation – this paper) or deformed (deformation > resolution – Dhuria and Misra in Eur Phys J C 75(1):16, arXiv:1406.6076 [hep-th], 2015) resolved warped deformed conifold, the local $$T^3$$ of Dhuria and Misra (JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013) in the MQGP limit is the $$T^2$$ -invariant special Lagrangian three-cycle of Ionel and Min-OO (Ill J Math 52(3), 2008) justifying the construction in Dhuria and Misra (JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013) of the delocalized Strominger–Yau–Zaslow Type IIA mirror of the Type IIB background of Mia et al. (Nucl Phys B 839:187, arXiv:0902.1540 [hep-th], 2010).
Highlights
The AdS/CFT correspondence or in general the gauge/gravity duality has proved to be a very useful tool in understanding the properties of super Yang–Mills theory at large ’t Hooft coupling
Building up on the Klebanov–Witten [8], Klebanov–Nekrasov [9] and Klebanov–Tseytlin [10] models, a logarithmic RG flow just like QCD was obtained in the non-conformal Klebanov–Strassler model [11] by considering M fractional D3 branes along with N D3 branes in a conifold geometry wherein the IR geometry was modified resulting in a deformed conifold
From the knowledge of quasinormal modes associated with the vector modes of metric perturbations obtained by imposing Dirichlet boundary condition at the asymptotic boundary, on an appropriate gauge-invariant perturbation constructed using the prescription of [5], we have computed for the first time, in the context of the same top–down largeN holographic thermal QCD at finite gauge coupling uplifted to M-theory, the non-conformal corrections to the shear mode diffusion constant up to NLO in N
Summary
The AdS/CFT correspondence or in general the gauge/gravity duality has proved to be a very useful tool in understanding the properties of super Yang–Mills theory at large ’t Hooft coupling. From the knowledge of quasinormal modes associated with the vector modes of metric perturbations obtained by imposing Dirichlet boundary condition at the asymptotic boundary, on an appropriate gauge-invariant perturbation constructed using the prescription of [5], we have computed for the first time, in the context of the same top–down largeN holographic thermal QCD at finite gauge coupling uplifted to M-theory, the non-conformal corrections to the shear mode diffusion constant up to NLO in N. We have evaluated for the first time in the context of the aforementioned M-theory uplift corresponding to finite gs, the non-conformal temperature-dependent correction at the NLO in N , to the shear viscosity η and shear-viscosity–entropy-density ratio η s from the twopoint energy-momentum tensor correlation function corresponding to the tensor mode of the metric perturbation.
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