The N > 2 supersymmetric AdS vacua in maximal supergravity

We perform a systematic search for anti-de Sitter vacua of maximal super-gravity 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 W-rotated SO(8) (N = 3) and SO(1, 7) (N = 4 and 3) gauged models. All vacua disappear in the W -> 0 limit. 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.