Moduli Stabilization, Large-Volume dS Minimum Without anti-D3-Branes, (Non-)Supersymmetric Black Hole Attractors and Two-Parameter Swiss Cheese Calabi-Yau's

Understand

We consider issues of moduli stabilization and "area codes" for type II flux compactifications, and the "Inverse Problem" and "Fake Superpotentials" for extremal (non)supersymmetric black holes in type II compactifications on (orientifold of) a compact two-parameter Calabi-Yau expressed as a degree-18 hypersurface in WCP^4[1,1,1,6,9] which has multiple singular loci in its moduli space.

• We argue the existence of extended "area codes" [1] wherein for the same set of large NS-NS and RR fluxes, one can stabilize all the complex structure moduli and the axion-dilaton modulus (to different sets of values) for points in the moduli space away as well as near the different singular conifold loci leading to the existence of domain walls.
• Using techniques of [3] we explicitly show that given a set of moduli and choice of a gauge(the superpotential) corresponding to an extremal black hole, one can actually work out the corresponding charges (of the extremal black hole) - the so-called "inverse problem".
• We also show the existence of "fake superpotentials" [4] corresponding to non-BPS extremal black-hole solutions corresponding to the aforementioned Calabi-Yau three-fold.