Type IIB on $S^3\times S^3$ through $Q$ & $P$ fluxes

We study a class of orientifold compactifications of type IIB supergravity with fluxes down to 4D in connection with truncations of half-maximal gauged supergravities yielding isotropic STU-models with minimal supersymmetry. In this context, we make use of a group-theoretical approach in order to derive flux-induced superpotentials for different IIB backgrounds. We first review the toroidal case yielding GKP-like superpotentials characterised by their \emph{no-scale} behaviour. We then turn to $S^3\times S^3$ and $S^{3} \times $\mathbb{T}$^{3}$, which, surprisingly, give rise to effective descriptions of non-geometric $Q$- and $P$-fluxes through globally geometric non-toroidal compactifications. As a consequence, such constructions break the no-scale symmetry without invoking any non-perturbative effects.