More stable dS vacua from S-dual non-geometric fluxes

TL;DR

This work investigates stable vacua in Type IIB string theory on anisotropic T^6/Z_2 orientifolds with RR, NS-NS and S-dual non-geometric Q and P fluxes, seeking minima of the 4D scalar potential using a genetic algorithm. It reports 11 AdS and 7 dS vacua across isotropic, semi-isotropic, and anisotropic torus geometries, with a consistent moduli mass hierarchy where complex-structure moduli are typically heavier than the Hubble scale in dS cases. The dS solutions are BF-stable and exhibit large F-terms and gravitino masses, while the axio-dilaton and Kähler moduli emerge as potential small-field inflaton candidates; several vacua reside without brane sources, hinting at possible uplift to extended ${\cal N}=4$ theories. The results illuminate how non-geometric fluxes and S-duality can stabilize moduli and generate a landscape of vacua, though a full 10D derivation and expansion to broader flux spaces remain for future work.

Abstract

Stable vacua obtained from isotropic tori compactification might not be fully stable provided the existence of runaway directions in the Kaehler directions of anisotropy. By implementing a genetic algorithm we report the existence of explicit flux configurations leading to stable de Sitter and Anti- de Sitter vacua, consisting on Type IIB compactifications on a 6-dimensional anisotropic torus threaded with standard and S-dual invariant non-geometric fluxes in the presence of orientifold 3-planes. In all dS vacua the masses of the complex structure moduli are heavier than the Hubble scale suggesting that the axio-dilaton and Kaeahler moduli are natural candidates for small-field inflation. In the way, we also report new solutions on isotropic and semi-isotropic tori compactifications. Finally, we observe that, since all our solutions are obtained in the absence of solitonic objects, they are good candidates to be lifted to stable solutions in extended supersymmetric theories.