Topics in Supergravity Phenomenology

In the first part of the review article, we discuss the possibility of realizing "mu-split-like SUSY" scenario from a phenomenological model, which we show could be realizable locally as the large volume limit of a type IIB Swiss-Cheese Calabi-Yau orientifold involving a mobile space-time filling D3-brane localized at a nearly special Lagrangian three-cycle embedded in the "big" divisor and multiple fluxed stacks of space-time filling D7-branes wrapping the same "big" divisor. We show that the mass of one of the Higgs doublets can be produced to be of the order of 125 GeV whereas other Higgs as well as higgsino mass parameter to be very heavy- the "mu-split-like SUSY" scenario. Then we discuss the role of the heavy squarks/sleptons and the light Higgs in (i) obtaining long-lived gluinos (ii) in verifying that the NLSPs (squarks/sleptons/neutralino) decay into the LSP (gravitino) respects the BBN constraints with the lifetime of the LSP (gravitino) coming out to be of the order or larger than the age of the universe, (iii) getting gravitino relic abundance of around 0.1, and (iv) obtaining electronic EDM close to the experimental upper bounds. In second part of the review article, we obtain local M-theory uplift of Type IIB background involving non-compact (resolved) warped deformed conifold and (N) space time filling D3-branes placed on the singularity of the conifold, (M) D5-branes wrapped around compact 2-sphere, and (N_f) D7-branes wrapped around non-compact four-cycle via Strominger-Yau-Zaslow's mirror symmetry prescription and show the stability of the solution so obtained. We propose a new MQGP limit corresponding to finite-string-coupling (g_s~ 1)- large-t'Hooft-coupling regime of M-theory. Interestingly, we obtain eta/s=1/4 pi for the uplift and the diffusion constant D~1/T for types IIB/IIA backgrounds in the both limits