Critical points of maximal D=8 gauged supergravities

We study the general deformations of maximal eight-dimensional supergravity by using the embedding tensor approach. The scalar potential induced by these gaugings is determined. Subsequently, by combining duality covariance arguments and algebraic geometry techniques, we find the complete set of critical points of the scalar potential. Remarkably, up to SO(2) X SO(3) rotations there turns out to be a unique theory admitting extrema. The gauge group of the theory is CSO(2,0,1).Comment: 14 pages. v2: minor changes - published versio

Charting the landscape of N=4 flux compactifications

We analyse the vacuum structure of isotropic Z_2 x Z_2 flux compactifications, allowing for a single set of sources. Combining algebraic geometry with supergravity techniques, we are able to classify all vacua for both type IIA and IIB backgrounds with arbitrary gauge and geometric fluxes. Surprisingly, geometric IIA compactifications lead to a unique theory with four different vacua. In this case we also perform the general analysis allowing for sources compatible with minimal supersymmetry. Moreover, some relevant examples of type IIB non-geometric compactifications are studied. The computation of the full N=4 mass spectrum reveals the presence of a number of non-supersymmetric and nevertheless stable AdS_4 vacua. In addition we find a novel dS_4 solution based on a non-semisimple gauging.Comment: Minor corrections and references added. Version published in JHE