Algebras and non-geometric flux vacua

In this work we classify the subalgebras satisfied by non-geometric Q-fluxes in type IIB orientifolds on T/(Z2 × Z2) with three moduli (S, T, U). We find that there are five subalgebras compatible with the symmetries, each one leading to a characteristic flux-induced superpotential. Working in the 4-dimensional effective supergravity we obtain families of supersymmetric AdS4 vacua with all moduli stabilized at small string coupling gs. Our results are mostly analytic thanks to a judicious parametrization of the non-geometric, RR and NSNS fluxes. We are also able to leave the flux-induced C4 and C8 RR tadpoles as free variables, thereby enabling us to study which values are allowed for each Q-subalgebra. Another novel outcome is the appearance of multiple vacua for special sets of fluxes. However, they generically have gs > 1 unless the net number of O3/D3 or O7/D7 sources needed to cancel the tadpoles is large. We also discuss briefly the issues of axionic shift symmetries and cancellation of Freed-Witten anomalies.