Minkowski flux vacua of type II supergravities

We study flux compactifications of 10d type II supergravities to 4d Minkowski space-time, supported by parallel orientifold Op-planes with 3 $\leq$ p $\leq$ 8. With some restrictions, the 4d Ricci scalar can be written as a negative sum of squares involving BPS-like conditions. Setting all squares to zero provides automatically a solution to 10d equations of motion. This way, we characterize a broad class, if not the complete set, of Minkowski flux vacua. We also conjecture an extension to include non-geometric fluxes. None of our results rely on supersymmetry.