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`Towards Big Divisor Swiss Cheese mu-Split Supersymmetry Scenario'

Abstract: Starting with type IIB string theory compactified on an
orientifold of a Swiss-Cheese Calabi-Yau expressed as a degree-18
hypersurface in the weighted complex projective space
WCP^4[1,1,1,6,9], in the presence of a mobile space-time filling
D3-brane and fluxed [stack(s) of] space-time filling D7-brane(s)
wrapping the 'big' (as opposed to the 'small') divisor, we give a
geometric proposal for obtaining a super-massive gravitino in the
inflationary epoch and a "light" gravitino in the present era in a
single setup. We  also show that the setup naturally realizes a
"mu-split supersymmetry scenario"  wherein having restricted the
mobile D3-brane to the big divisor, one obtains super-massive D3-brane
positon moduli - identified as the two Higgs doublets - at the string
scale and after 1-loop  Nath-Arnowitt RG-evolution to the EW scale,
one obtains one light and one super-massive Higgs doublet. Also, the
fermions (quarks/leptons)  corresponding to the fermionic
super-partners of the Wilson line moduli, are very light but the
Higgsino mass parameter is very large. I also discuss issues like
neutrino masses, gluino  and proton decays. As a bonus, I will discuss
obtaining the geometric Kaehler potential (relevant to the moduli
space Kaehler potential in the presence of a mobile D3-brane)
corresponding to a Ricci-flat metric for the Swiss-Cheese Calabi-Yau
used in the large volume limit  using Gauged Linear Sigma Model
techniques for obtaining the geometric Kaehler potential for the big
divisor, and the Donaldson's algorithm for obtaining Ricci-flat
metrics, as guides. 
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