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

TL;DR

This work analyzes moduli stabilization in type II flux compactifications on a two-parameter Swiss Cheese Calabi-Yau, demonstrating extended area codes where the same fluxes stabilize complex structure and axion-dilaton at finitely separated points, connected by domain walls. By incorporating non-perturbative $\alpha'$-corrections and instanton effects, it shows the possibility of a large-volume non-supersymmetric dS minimum without anti-D3 uplifting. The paper also develops the inverse problem for extremal black holes, providing explicit charge configurations corresponding to given moduli and revealing non-unique (fake) superpotentials that describe non-BPS attractors. Together, these results illuminate how fluxes, instantons, and duality structures can yield stable de Sitter vacua and rich black-hole attractor physics in multi-parameter Calabi-Yau compactifications.

Abstract

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. By including non-perturbative alpha' and instanton corrections in the Kaehler potential and superpotential [2], we show the possibility of getting a large-volume non-supersymmetric (A)dS minimum - a dS minimum without the addition of anti-D3 branes a la KKLT. The chosen Calabi-Yau has been of relevance also from the point of other studies of stabilization of the Kaehler moduli via nonperturbative instanton contributions [5] and the possibility of getting non-supersymmetric AdS vacua (and their subsequent dS-uplifts) using (alpha')^3 corrections to the Kaehler potential [6,7,8].