Lobotomy of flux compactifications

We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on $ \mathbb{T} $ 6 with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge algebra. Besides the known four AdS solutions surviving the orientifold projection to $ \mathcal{N} $ = 4 induced by O6-planes, this theory contains a novel AdS solution that requires non-trivial orientifold-odd fluxes, hence being a genuine critical point of the $ \mathcal{N} $ = 8 theory