Abstract
The SYZ mirror, in the `delocalized limit' of [1], of (M)N (fractional)D3-branes, and wrapped N_f flavor D7-branes in the presence of a black-hole resulting in a non-Kaehler resolved warped deformed conifold (NKRWDC) in [2], was carried out in [3] and resulted in black M3-branes. The uplift, if valid globally(like [4] for fractional D3 branes in conifolds), asymptotes to M5-branes wrapping a two-cycle (homologously an (large) integer sum of two-spheres) in AdS_5xM_6. Interestingly, in the MQGP limit, assuming the deformation > resolution, by estimating the five SU(3) structure torsion (\tau) classes W_{1,2,3,4,5} we show that \tau\in W_4+W_5: 2/3 Re(W^3bar_5)=W^3bar_4 in the UV, implying the NKRWDC locally preserves SUSY. Further, the local T^3 of [3] in the large-r limit and the `MQGP' limit of [3], satisfies the same conditions as the maximal T^2-invariant special Lagrangian three-cycle of T^*(S^3) of [6], partly justifying use of local SYZ mirror symmetry in [3]. Using the Ouyang embedding in the DBI action of a D7-brane or by dimensionally reducing the 11-dimensional EH action to five (R^{1,3},r) dimensions, we then calculate a variety of gauge and metric-perturbation-modes' two-point functions using the prescription of [5], and show: (i) diffusion constant D~1/T, (ii) the electrical conductivity \sigma~T, (iii) the charge susceptibility \chi~ T^2, (iv) [using (i) - (iii)] the Einstein's relation \sigma/\chi=D, is indeed satisfied, (v) the R-charge diffusion constant D_R~1/T, and (vi) the possibility of generating \eta/s=1/4pi from solutions to the vector and tensor mode metric perturbations' EOMs, separately. All results are also valid in the limit of [2].
Highlights
Since the formulation of the AdS/CFT correspondence [1–3], it has been of profound interest to gain theoretical insight into the physics of a strongly coupled Quark Gluon Plasma produced in heavy-ion collisions at RHIC by using holographic techniques
First, by calculating the five SU (3) structure torsion (τ ) classes W1,2,3,4,5, we show that in the MQGP limit of [26] and assuming the deformation parameter to be larger than the resolution parameter, the non-Kähler resolved warped deformed conifold of [24], in the large-r limit, reduces to a warped Kähler deformed conifold for which τ ∈ W5
Given the strong-coupling nature of QGP it is believed that this will be better described in the limit of finite gauge coupling [27]
Summary
3], it has been of profound interest to gain theoretical insight into the physics of a strongly coupled Quark Gluon Plasma (sQGP) produced in heavy-ion collisions at RHIC by using holographic techniques Within this context, the holographic spectral functions play an important role because of their ability to provide a framework to compute certain transport properties of QGP, such as the conductivity and viscosity of the plasma which otherwise are not computationally tractable. The methodology to calculate two-point Green functions by applying gauge–gravity duality has been developed in the series of papers [4,5,6] by considering D3-brane background. This approach is useful for transport coefficients that are universal within models with gravity duals. Though the bound was initially obtained by assuming a zero charge density, the same was shown to hold
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