Flux moduli stabilisation, supergravity algebras and no-go theorems

We perform a complete classification of the flux-induced 12d algebras compatible with the set of mathcal{N} = 1 type II orientifold models that are T-duality invariant, and allowed by the symmetries of the mathbb {T}^6/ mathbb {Z}_2 × mathbb {Z}_2 isotropic orbifold. The classification is performed in a type IIB frame, where only {bar H_3} and Q fluxes are present. We then study no-go theorems, formulated in a type IIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By deriving a dictionary between the sources of potential energy in types IIB and IIA, we are able to combine algebra results and no-go theorems. The outcome is a systematic procedure for identifying phenomenologically viable models where Mkw/dS vacua may exist. We present a complete table of the allowed algebras and the viability of their resulting scalar potential, and we point at the models which stand any chance of producing a fully stable vacuum.