Supermembranes with fewer supersymmetries

The usual supermembrane solution of D = 11 supergravity interpolates between R11 and AdS4 × round R7, has symmetry P3 × SO(8) and preserves 12 of the spacetime supersymmetries for either orientation of the round S7. Here we show that more general supermembrane solutions may be obtained by replacing the round S7 by any seven-dimensional Einstein space M7. These have symmetry P3 × G, where G is the isometry group of M7. For example, G = SO(5) × SO(3) for the squashed S7. For one orientation of M7, they preserve N16 spacetime supersymmetries where 1 ≤ N ≤ 8 is the number of Killing spinors on M7; for the opposite orientation they preserve no supersymmetries since then M7 has no Killing spinors. For example N = 1 for the left-squashed S7 owing to its G2 Weyl holonomy, whereas N = 0 for the right-squashed S7. All these solutions saturate the same Bogomolʹnyi bound between the mass and charge. Similar replacements of SD-p-2 by Einstein spaces MD-p-2 yield new super p-brane solutions in other spacetime dimensions D ≤ 11. In particular, simultaneous dimensional reduction of the above D = 11 supermembranes on S1 leads to a new class of D = 10 elementary string solutions which also have fewer supersymmetries.