Four curious supergravities

We consider four supergravities with 16 + 16, 32 + 32, 64 + 64, 128 + 128 degrees of freedom displaying some curious properties: (1) They exhibit minimal supersymmetry (N = 1, 2, 2, 1) but maximal rank (r = 7, 6, 4, 0) of the scalar coset in D = 4, 5, 7, 11. (2) They couple naturally to supermembranes and admit these membranes as solutions. (3) Although the D = 4, 5, 7 supergravities follow from truncating the maximally supersymmetric ones, there nevertheless exist M-theory compactifications with G(2), SU(3), SU(2) holonomy having these supergravities as their massless sectors. (4) They reduce to N = 1, 2, 4, 8 theories all with maximum rank 7 in D = 4 which (5) correspond to 0, 1, 3, 7 lines of the Fano plane and hence admit a division algebra (R, C, H, O) interpretation consistent with the black-hole/qubit correspondence, (6) are generalized self-mirror, and hence (7) have a vanishing on-shell trace anomaly.