Supermembranes with fewer supersymmetries

The usual supermembrane solution of D = 11 supergravity interpolates between R(11) and AdS(4) x round S-7, has symmetry P-3 x SO(8) and preserves 1/2 of the spacetime supersymmetries for either orientation of the round S-7. Here we show that more general supermembrane solutions may be obtained by replacing the round S-7 by any seven-dimensional Einstein space M(7). These have symmetry P-3 X G, where G is the isometry group of M(7). For example, G = SO(5) x SO(3) for the squashed S-7. For one orientation of M(7), they preserve N/16 spacetime supersymmetries where 1 less than or equal to N less than or equal to 8 is the number of Killing spinors on M(7); for the opposite orientation they preserve no supersymmetries since then M(7) has no Killing spinors. For example N = 1 for the left-squashed S-7 owing to its G(2) Weyl holonomy, whereas N = 0 for the right-squashed S-7. All these solutions saturate the same Bogomol'nyi bound between the mass and charge. Similar replacements of S-D-p-2 by Einstein spaces M(D-p-2) yield new super p-brane solutions in other spacetime dimensions D less than or equal to 11. In particular, simultaneous dimensional reduction of the above D = 11 supermembranes on S-1 leads to a new class of D = 10 elementary string solutions which also have fewer supersymmetries.