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)=(,{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 =0,pi due to poles. Introducing a small-angle cut-off c and using the =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.Comment: 1+58 pages, LaTeX; v4 some minor corrections, results unchange

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The Strominger-Yau-Zaslow (SYZ) mirror, in the 'delocalised limit' of Becker et al. (Nucl Phys B 702:207, 2004), of N D3-branes, M fractional D3-branes and N f flavour D7-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(JHEP :001, 2013) and resulted in black M3-branes. There are two parts in our paper. In the first we show that in the 'MQGP' limit discussed in Dhuria and Misra (ii) Assuming the deformation parameter to be larger than the resolution parameter, by estimating the five SU (3) structure torsion (τ ) classes W 1,2,3,4,5 we verify that τ ∈ W 5 in the large-r limit, implying the NKRWDC reduces to a warped Kähler deformed conifold. (iii) The local T 3 of Dhuria and Misra (JHEP 1311(JHEP :001, 2013) in the large-r limit satisfies the same conditions as the maximal T 2 -invariant special Lagrangian three-cycle of T * S 3 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(JHEP :001, 2013). In the second part of the paper, by either integrating out the angular coordinates of the non-compact four-cycle which a D7-brane wraps around, using the Ouyang embedding, in the DBI action of a D7-brane evaluated at infinite radial boundary, or by dimensionally reducing the 11-dimensional EH action to five (R 1,3 , r ) dimensions and at the infinite radial boundary, we then calculate in particular the g s < ∼ 1 a

We show that it is possible to realize a "µ-split SUSY" scenario [1] in the context of large volume limit of type IIB compactifications on Swiss-Cheese Calabi-Yau orientifolds in the presence of a mobile spacetime filling D3-brane and a (stack of) D7-brane(s) wrapping the "big" divisor. For this, we investigate the possibility of getting one Higgs to be light while other to be heavy in addition to a heavy Higgsino mass parameter. Further, we examine the existence of long lived gluino that manifests one of the major consequences of µ-split SUSY scenario, by computing its decay width as well as lifetime corresponding to the three-body decays of the gluino into either a quark, a squark and a neutralino or a quark, squark and Goldstino, as well as two-body decays of the gluino into either a neutralino and a gluon or a Goldstino and a gluon. Guided by the geometric Kähler potential for Σ B obtained in [2] based on GLSM techniques, and the Donaldson's algorithm [3] for obtaining numerically a Ricci-flat metric, we give details of our calculation in [4] pertaining to our proposed metric for the full Swiss-Cheese Calabi-Yau (the geometric Kähler potential being needed to be included in the full moduli space Kähler potential in the presence of the mobile space-time filling D3-brane), but for simplicity of calculation, close to the big divisor, which is Ricci-flat in the large volume limit. Also, as an application of the one-loop RG flow solution for the Higgsino mass parameter, we show that the contribution to the neutrino masses at the EW scale from dimension-six operators arising from the Kähler potential, is suppressed relative to the Weinberg-type dimension-five operators.

The generic expectation in string/supergravity models is that there are multiple moduli fields with masses of the order of the supersymmetry breaking scale. We study the cosmology that arises as a result of vacuum misalignment of these moduli fields (in contrast to previous studies which mostly focussed on the single modulus case). We show that the dark radiation produced from the heavier moduli undergoes significant dilution. This happens even if there is a small splitting between the masses of the lightest and the heavier moduli. On the other hand, in the absence of fast annihilation processes decay of heavier moduli generically leads to overproduction of dark matter. We discuss a scenario where the problem can be addressed with a prompt dark matter annihilation to dark radiation. This can lead to realistic dark matter abundances, and the additional dark radiation produced as a result of this mechanism undergoes sufficient dilution as long as the annihilation is prompt.