ON ISSUES IN SWISS CHEESE COMPACTIFICATIONS

We give a brief review of our previous works.(1,2) We discuss two sets of issues. The first has to do with the possibility of getting a non-supersymmetric dS minimum with- out the addition of (D3) over bar -branes as in KKLT, and axionic slow-roll inflation, in type II flux compactifications. The second has to do with the "Inverse Problem"(3) and "Fake Superpotentials"(4) for extremal (non)supersymmetric black holes in type II compactific ations.We use (orientifold of) a "Swiss Cheese" Calabi-Yau(5) expressed as a degree-18 hypersurface in WCP4[1,1,1,6,9] in the "large-volume-scenario" limit(6) for the former.