  For the Ouyang embedding we calculate the chemical potential mu_C due to a
U(1) gauge field on the w.v. of N_f D7-branes wrapped around a 4-cycle in a
resolved warped deformed conifold with (M)N (fractional)D3-branes of [1], and
show the possible thermodynamical stability up to linear order in the embedding
parameter. In the spirit of [2] we obtain the local type IIA mirror using SYZ
mirror symmetry near (theta_{1,2},psi)=(<theta_{1,2}>,{0,2pi,,4pi}) and then
oxidize the same to M theory. We take two limits of this
uplift:(i)g_s,g_sN_f,g_sM^2/N,g_s^2M N_f<<1,g_sM,g_sN>>1 similar to [1]
effected by M eps^{-3d/2}, N eps^{-19d},g_s epsn^d,d>0 and eps<=O(0.01);(ii)the
`MQGP limit' g_sM^2/N<<1, g_sN>>1 for finite g_s,M, effected by: g_s eps, M
eps^{-3d/2},N eps^{-39d},d>0, eps<~1). The second limit is more suited for the
study of QGP (See [3]) and can only be addressed in M theory. The uplift gives
a black M3-brane solution whose near-horizon geometry near
theta_{1,2}=0,pi-branches, preserves 1/8 SUSY. We obtain eta/s=1/4pi for the
uplift and the diffusion constant for types IIB/IIA backgrounds comes out to be
~1/T, for both limits. The D=11 SUGRA action up to O(R^4,|G_4|^2) is expected
to receive dominant contributions near <theta_{1,2}>=0,pi due to poles.
Introducing a small-angle cut-off c and using the <theta_{1,2}>=c,(pi-c)-local
uplift the specific heat from the IR-finite part of the action (c-independent)
turns out to be positive indicative of the thermodynamical stability of the
uplift. An ALD-gravity-type interpretation can be given to the counter-terms
for(i). Its verified that the black M3-brane entropy S r_h^3 from M-theoretic
thermodynamical methods and the horizon areas of types IIB/IIA/M3-brane
solutions.
