**75**: 16

https://doi.org/10.1140/epjc/s10052-014-3207-6

Regular Article - Theoretical Physics

## Transport coefficients of black MQGP -branes

^{1}
Theoretical Physics Division, Physical Research Laboratory, Ahmedabad, 380 009, India

^{2}
Department of Physics, Indian Institute of Technology, Roorkee, 247 667, Uttaranchal, India

^{*} e-mail: aalokfph@iitr.ac.in

Received:
25
September
2014

Accepted:
27
November
2014

Published online:
14
January
2015

The Strominger–Yau–Zaslow (SYZ) mirror, in the ‘delocalised limit’ of Becker et al. (Nucl Phys B 702:207, 2004), of -branes, fractional -branes and flavour -branes wrapping a non-compact four-cycle in the presence of a black hole (BH) resulting in a non-Kähler resolved warped deformed conifold (NKRWDC) in Mia et al. (Nucl Phys B 839:187, 2010), was carried out in Dhuria and Misra (JHEP 1311:001, 2013) and resulted in black -branes. There are two parts in our paper. In the first we show that in the ‘MQGP’ limit discussed in Dhuria and Misra (JHEP 1311:001, 2013) a finite (and hence expected to be more relevant to QGP), finite and very large , and very small , we have the following. (i) The uplift, if valid globally (like Dasgupta et al., Nucl Phys B 755:21, 2006) for fractional branes in conifolds), asymptotically goes to -branes wrapping a two-cycle (homologously a (large) integer sum of two-spheres) in . (ii) Assuming the deformation parameter to be larger than the resolution parameter, by estimating the five structure torsion () classes we verify that in the large- limit, implying the NKRWDC reduces to a warped Kähler deformed conifold. (iii) The local of Dhuria and Misra (JHEP 1311:001, 2013) in the large- limit satisfies the same conditions as the maximal -invariant special Lagrangian three-cycle of of Ionel and Min-OO (J Math 52(3), 2008), partly justifying use of SYZ-mirror symmetry in the ‘delocalised limit’ of Becker et al. (Nucl Phys B 702:207, 2004) in Dhuria and Misra (JHEP 1311:001, 2013). In the second part of the paper, by either integrating out the angular coordinates of the non-compact four-cycle which a -brane wraps around, using the Ouyang embedding, in the DBI action of a -brane evaluated at infinite radial boundary, or by dimensionally reducing the 11-dimensional EH action to five () dimensions and at the infinite radial boundary, we then calculate in particular the (part of the ’MQGP’) limit, a variety of gauge and metric-perturbation-modes’ two-point functions using the prescription of Son and Starinets (JHEP 0209:042, 2002). We hence study the following. (i) The diffusion constant , (ii) the electrical conductivity , (iii) the charge susceptibility , (iv) [using (i)–(iii)] the Einstein relation , (v) the R-charge diffusion constant , and (vi) (using Dhuria and Misra, JHEP 1311:001, 2013) and Kubo’s formula related to shear viscosity ) the possibility of generating from solutions to the vector and tensor mode metric perturbations’ EOMs, separately. The results are also valid for the limits of Mia et al. (Nucl Phys B 839:187, 2010): , .

*© SIF and Springer-Verlag Berlin Heidelberg, 2015*