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).