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The N>2 supersymmetric AdS vacua in maximal supergravity

We perform a systematic search for anti-de Sitter vacua of maximal supergravity with N>2 residual supersymmetries. We find that maximal supergravity admits two 1-parameter classes of N=3 and N=4 vacua, respectively. They are embedded, for the different values of an angular parameter, in the $ω$-rotated SO(8) (N=3) and SO(1,7) (N=4 and 3) gauged models. All vacua disappear in the limit when $ω$ tends to zero. We determine the mass spectra and the AdS-supermultiplet structure. These appear to be the first and only N>2 supersymmetric AdS vacua in maximal supergravity, aside from the N=8 vacua of the SO(8)-gauged models. We also prove on general grounds that no such vacua can exist for 4<N<8.