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 $O_p$ planes with $3\le p\le 8$. With some geometric restrictions, the 4D Ricci scalar can be written as a negative sum of squares involving Bogomol’nyi-Prasad-Sommerfield-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 with parallel orientifolds. We conjecture an extension with nongeometric fluxes. None of our results rely on supersymmetry.